Professor Celso Grebogi

Professor Celso Grebogi The University of Aberdeen School of Natural & Computing Sciences Professor Celso Grebogi Sixth Century Chair in Nonlinear & Comp work +44 (0)1224 272791 work fax +44 (0)1224 272943 pref Institute for Complex Systems and Mathematical Biology School of Natural and Computing Sciences King's College University of Aberdeen Old Aberdeen AB24 3UE, UK

Sixth Century Chair Professor
Director, Institute for Complex Systems and Mathematical Biology

CEng, MS, PhD, DrHC, FRSE, FAPS, FABC, FTWAS, FInstP

Professor Celso Grebogi

Personal Details

Telephone: +44 (0)1224 272791
Fax: +44 (0)1224 272943
Email: grebogi@abdn.ac.uk
Address: Institute for Complex Systems and Mathematical Biology
School of Natural and Computing Sciences
King's College
University of Aberdeen
Old Aberdeen AB24 3UE, UK
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Biography

Professor Celso Grebogi earned his bachelor's degree in chemical engineering from the Universidade Federal do Parana in Curitiba (Brazil) in 1970. He became then "Professor Auxiliar" in the Departamento de Fisica at the Pontificia Universidade Catolica in Rio de Janeiro, where he remained until 1974. Professor Grebogi decided to pursue graduate studies in the United States after he was awarded the Fulbright Fellowship. He received his M.S. and Ph.D. degrees from the Department of Physics and Astronomy, University of Maryland at College Park. After obtaining his doctoral degree in 1978, he joined the University of California at Berkeley as a post-doctoral fellow. In 1981, Professor Grebogi returned to the University of Maryland as a faculty, but joined the Department of Mathematics as a Professor in 1990, with joint appointments at the Institute for Plasma Research and the Institute for Physical Science and Technology. He has remained at the University of Maryland as a Full Professor until 2001 when he resigned to go back to Brazil as Full Professor at the Institute of Physics, University of Sao Paulo. In 2005, he was invited to join the University of Aberdeen as the "Sixth Century Chair in Nonlinear and Complex Systems".

Professor Grebogi did extensive research in the field of plasma physics before his work on chaotic dynamics. Professor Grebogi's research on chaotic dynamical systems combines analytical methods and techniques with extensive computer experiments utilizing state-of-the-art computational facilities. The objective of the research is to establish basic mathematical principles so that scientists and engineers can then apply these principles to understand and analyze the systems they are investigating in their own fields. Using this approach Professor Grebogi has obtained a number of important results e.g.: the establishment of "crises" is the fundamental process by which chaotic attractors undergo sudden changes as a system parameter varies; the mathematical theory and experimental verification of how transient chaos phenomena are likely to manifest themselves in practice; and the work on fractal basin boundaries that pointed out the important practical consequences of this type of boundary. The current research focuses on systems biology, methods to control chaos, the dynamics of spatio-temporal systems, active processes in chaotic flows, and the rigorous determination of how long actual trajectories of a chaotic process stay near a given numerical trajectory, i.e. the problem of shadowing. Professor Grebogi has also been arguing that, when analyzing systems which exhibit irregular behavior, modeling must be expanded to include algorithms which make use of measured time series. These ideas which include observation, analysis, and control of chaotic systems have been widely implemented by experimental scientists and engineers.

In recognition of Professor Grebogi's scientific accomplishments, which amounted to over three hundred publications, and the delivery of over three hundred invited lectures at international conferences and at universities and other institutions, he received many awards, prizes, and other distinctions. Among them, he was recipient of the Doctor Honoris Causa Degree (Dr. re. nat. h. c.) from the University of Potsdam - Germany, Honorary Professorship from University of Aberdeen - Scotland, Toshiba Chair as a World-renowned Scholar from the Waseda University - Japan, Humboldt Senior Prize from Germany, and selected as a University of Maryland Distinguished Research Faculty. He is also Fellow of The Royal Society of Edinburgh, Fellow of the American Physical Society, Fellow of the Brazilian Academy of Sciences, Fellow of TWAS - The Academy of Sciences for the Developing World, Fellow of the Institute of Physics (UK), and Elected Fellow (Mitglied) of the Max Planck Society. He is a Thompson-ISI Highly Cited Author with over 17,000 citations. His H-index is 63.

 

Summary

  • B. Eng.,Chemical Engineering, Federal University of Parana, 1970
  • Adjunct Professor, Pontifical Catholic University, 1971-1974
  • M.S., Physics, University of Maryland 1975
  • Ph.D., Physics, University of Maryland, 1978
  • Post-doctoral Research Fellow, University of California at Berkeley, 1978-1981
  • Research Scientist, University of Maryland, 1981-1990
  • Associate Professor of Mathematics, University of Maryland, 1990-1993
  • Full Professor of Mathematics, University of Maryland, 1993-2001
  • Consultant for the US Navy, 1983-1995
  • Visiting Scientist, University of California at Santa Barbara, 1984
  • Consultant, Lawrence Livermore National Laboratory, 1984-1985
  • Consultant, Science Applications International, 1986-1988
  • Visiting Scholar, Waseda University, 1996
  • Visiting Professor, University of Potsdam, 1996-1997
  • Professeur Invite, Universite du Havre, 2001
  • Professor Titular, University of Sao Paulo, 2001-2005
  • Sixth Century Chair in Nonlinear and Complex Systems, University of Aberdeen, since 2005
  • Director of theNonlinear Dynamics and Complex Systems Group. The Northern Ressearch Partnership of Scottish Universities, 2007-2010
  • Director of the Institute for Complex Systems and Mathematical Biology, since 2009
  • Adjunct Professor, Institute of Medical Engineering, Xi'an Jiaotong University, 2010-2013
  • External Fellow of the Freiburg Institute for Advanced Studies, 2011-2012

Awards and Honours

  • Fulbright Fellowship, 1974
  • Distinguished Scientist Lecturer, Carnegie Mellon University, 1989
  • Fellow of the American Physical Society, 1991
  • Toshiba Chair as World-renowned Scholar, 1995
  • North British Differential Equations Lecture Tour, 1996
  • Senior Humboldt Prize, 1996
  • Distinguished Faculty Research Fellow Award, University of Maryland, 1996
  • Doctor Honoris Causa, University of Potsdam, 1997
  • Elected Fellow (Mitglied), Max-Planck-Society, 1998
  • Fellow of the Brazilian Academy of Sciences, 2002
  • Humboldt Prize Revisited Award, 2003
  • Fellow of the Academy of Sciences for the Developing World (TWAS), 2004
  • Member of over a dozen Editorial Boards Associate Editorships over the years
  • Membership in various scientific societies
  • Milestone in the last 50 year: 1990 paper on Controlling Chaos, American Physical Society, 2008
  • Elected Honorary Member of the International Physics and Control Society, 2009
  • Elected Fellow of the Institute of Physics (UK), 2011
  • Elected Fellow of the Royal Society of Edinburgh, 2012
  • Thompson-ISI Highly Cited Author with over 17,000 citations and H-Index = 63

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Research Interests

Dynamics of nonlinear and complex systems including chaotic dynamics, fractal geometry, and systems biology.


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Research Grants

The dynamics of in-stent restenosis process, Medical Research Council, and many others


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External Responsibilities

  • Elected External Scientific Member, Max-Planck-Institute for the Physics of Complex Systems, since 1998
  • Associate Editor of the Philosophical Transactions of the Royal Society A, since 2005

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Selected Publications

  • “Universality in active chaos,” T. Tel, T. Nishikawa, A.E. Motter, C. Grebogi and Z. Toroczkai, Chaos 14, 72 (2004).
  • “Reactions in flows with nonhyperbolic dynamics,” A.P.S. Moura and C. Grebogi, Phys. Rev. E 70, 036216 (2004).
  • “Escaping from nonhyperbolic chaotic attractors,” S. Kraut and C. Grebogi, Phys. Rev. Lett. 92, 234101 (2004).
  • “Reactive particles in random flows,” G. Karolyi, T. Tel, A.P.S. Moura, and C. Grebogi, Phys. Rev. Lett. 92, 174101 (2004).
  • “Two-dimensional map for impact oscillator with drift,” E. Pavlovskaia and M. Wiercigroch, Phys. Rev. E 70, 036201 (2004).
  • “Chemical and biological activity in 3-dimensional flows,” A.P.S. Moura and C. Grebogi, Phys. Rev. E 70, 026218 (2004)
  • “Unstable dimension variability and codimension-one bifurcations of two-dimensional maps,” R.L. Viana, R. Barbosa and C. Grebogi, Phys. Lett. A 321, 244 (2004).
  • “Nonhyperbolic chaotic systems and synchronization,” E.E.N. Macau and C. Grebogi, Adv. Space Dynamics 4, 123 (2004).
  • ”Stability properties of nonhyperbolic chaotic attractors with respect to noise,” S. Kraut and C. Grebogi, Phys. Rev. Lett. 93, 250603 (2004).
  • “Bubbling bifurcation: loss of synchronization and shadowing breakdown in complex systems,” R.L. Viana, C. Grebogi, S. Pinto, S. Lopes, A. Batista and J. Kurths, Physica D 206, 94 (2005).
  • “Effective dynamics in Hamiltonian systems with mixed phase space,” A.E. Motter, A.P.S. Moura, C. Grebogi, and H. Kantz, Phys. Rev. E 71, 036215 (2005).
  • “Chemical and biological activity in open flows: a dynamical system approach,” T. Tel, A.P.S. Moura, C. Grebogi, and G. Karolyi, Physics Reports 413, 91 (2005).
  • “Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors,” M.S. Baptista, S. Kraut, and C. Grebogi, Phys. Rev. Lett. 95, 094101 (2005).
  • “Finite-size effects on open chaotic advection,” R.D. Vilela, A.P.S. Moura, and C. Grebogi, Phys. Rev. E 73, 026302 (2006).

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Publications

Contributions to Journals

Articles

  • Richard, M., Fryett, MR., Miller, S., Booth, I., Grebogi, C. & de Moura, APS. (2012). 'Optimality of DNA repair'. Journal of Theoretical Biology, vol 292, pp. 39.
    [Online] DOI: 10.1016/j.jtbi.2011.08.024
  • Sommerlade, L., Thiel, M., Platt, B., Plano, A., Riedel, G., Grebogi, C., Timmer, J. & Schelter, B. (2012). 'Inference of Granger causal time-dependent influences in noisy multivariate time series'. Journal of Neuroscience Methods, vol 203, no. 1, pp. 173-185.
    [Online] DOI: 10.1016/j.jneumeth.2011.08.042
  • Karschau, J., De Almeida, C., Richard, MC., Miller, S., Booth, I., de Moura, APS. & Grebogi, C. (2011). 'A matter of life or death: modeling DNA damage and repair in bacteria'. Biophysical Journal, vol 100, no. 4, pp. 814-821.
    [Online] DOI: 10.1016/j.bpj.2010.12.3713
  • Guseva, K., Thiel, M., Miller, S., Grebogi, C. & de Moura, APS. (2011). 'Collective response of self-organized clusters of mechanosensitive channels'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 83.
    [Online] DOI: 10.1103/PhysRevE.83.020901
    [Online] AURA: PhysRevE.83.020901.pdf
  • Schelin, AB., Karolyi, G., de Moura, APS., Booth, N. & Grebogi, C. (in press). 'Are the fractal skeletons the explanation for the narrowing of arteries due to cell trapping in a disturbed blood flow?'. Computers in Biology and Medicine.
    [Online] DOI: 10.1016/j.compbiomed.2011.07.002
  • Yang, R., Huang, L., Lai, Y. & Grebogi, C. (2011). 'Abnormal electron paths induced by Klein tunneling in graphene quantum point contacts'. Physical Review B Condensed Matter and Materials Physics, vol 84, no. 3.
    [Online] DOI: 10.1103/PhysRevB.84.035426
  • Yang, R., Huang, L., Lai, Y. & Grebogi, C. (2011). 'Quantum chaotic scattering in graphene systems'. Europhysics Letters, vol 94, no. 4.
    [Online] DOI: 10.1209/0295-5075/94/40004
  • Wang, W., Yang, R., Lai, Y., Kovanis, V. & Grebogi, C. (2011). 'Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing'. Physical Review Letters, vol 106, no. 15.
    [Online] DOI: 10.1103/PhysRevLett.106.154101
  • Huang, L., Lai, Y. & Grebogi, C. (2011). 'Characteristics of level-spacing statistics in chaotic graphene billiards'. Chaos, vol 21, no. 1.
    [Online] DOI: 10.1063/1.3537814
  • Grebogi, C. (2011). 'Pattern formation, synchronisation, and outbreak of biodiversity in cyclically competing games'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 83, no. 1.
  • Brackley, CA., Ebenhoeh, O., Grebogi, C., Kurths, J., Moura, AD., Romano, MC. & Thiel, M. (2010). 'Introduction to Focus Issue: Dynamics in Systems Biology'. Chaos, vol 20, no. 4.
    [Online] DOI: 10.1063/1.3530126
  • Schelin, AB., Karolyi, G., de Moura, APS., Booth, N. & Grebogi, C. (2010). 'Fractal structures in stenoses and aneurysms in blood vessels'. Philosophical Transactions of the Royal Society of London. Series A, vol 368, no. 1933, pp. 5605-5617.
    [Online] DOI: 10.1098/rsta.2010.0268
  • Rodrigues, C., de Moura, APS. & Grebogi, C. (2010). 'Random fluctuation leads to forbidden escape of particles'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 82, no. 2.
    [Online] DOI: 10.1103/PhysRevE.82.026211
  • Rodrigues, C., Grebogi, C. & de Moura, APS. (2010). 'Escape from attracting sets in randomly perturbed systems'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 82, no. 4, pp. 046217.
    [Online] DOI: 10.1103/PhysRevE.82.046217
    [Online] AURA: PhysRevE.82.046217.pdf
  • Baptista, MDS., Kakmeni, FM. & Grebogi, C. (2010). 'Combined effect of chemical and electrical synapses in Hindmarsh-Rose neural networks on synchronization and the rate of information'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 82, no. 3, pp. 036203.
    [Online] DOI: 10.1103/PhysRevE.82.036203
  • Grebogi, C. & Lai, Y. (2010). 'Extensively chaotic motion in electrostatically-driven nanowires and applications'. IET Micro & Nano Letters, vol 10, no. 2, pp. 406-413.
    [Online] DOI: 10.1021/nl902775m
  • Ni, X., Yang, R., Wang, W., Lai, Y. & Grebogi, C. (2010). 'Basins of coexistence and extinction in spatially extended ecosystems of cyclically competing species'. Chaos, vol 20, no. 4.
    [Online] DOI: 10.1063/1.3526993
  • Romano Blasco, MC., Thiel, M., Stansfield, I. & Grebogi, C. (2009). 'Queueing phase transition: Theory of Translation'. Physical Review Letters, vol 102, no. 19, pp. 198104-198107.
    [Online] DOI: 10.1103/PhysRevLett.102.198104
  • Scheling, A., Karoly, G., de Moura, APS., Booth, NA. & Grebogi, C. (2009). 'Chaotic advection in blood flow'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics.
  • Rodrigues, C., de Moura, APS. & Grebogi, C. (2009). 'Emerging attractors and the transition from dissipative to conservative dynamics'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 80, no. 026205.
  • Medrano-T, RO., Moura, APS., Tel, T., Caldas, IL. & Grebogi, C. (2008). 'Finite-size particles, advection, and chaos:: a collective phenomenon of intermittent bursting'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 78, no. 056206.
    [Online] DOI: 10.1103/PhysRevE.78.056206
  • Biemond, JJB., Moura, APS., Karolyi, G., Grebogi, C. & Nijmeijer, H. (2008). 'Onset of chaotic advection in open flows'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 78.
    [Online] DOI: 10.1103/PhysRevE.78.016317
  • Cao, Q., Wiercigroch, M., Pavlovskaia, EE., Grebogi, C. & Thompson, JMT. (2008). 'The limit case response of the archetypal oscillator for smooth and discontinuous dynamics'. International Journal of Non-Linear Mechanics, vol 43, pp. 462-473.
    [Online] DOI: 10.1016/j.ijnonlinmec.2008.01.003
  • Scheling, A., de Moura, APS. & Grebogi, C. (2008). 'Transition to chaotic scattering: signatures in the differential crosssection'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 78, no. 046204.
  • Cao, Q., Wiercigroch, M., Pavlovskaia, EE., Grebogi, C. & Thompson, JMT. (2008). 'The limit case response of archetypal oscillator for smooth and discontinuous dynamics'. International Journal of Non-Linear Mechanics, vol 43, no. 6, pp. 462-473.
    [Online] DOI: 10.1016/j.ijnonlinmec.2008.01.003
  • Vilela, RD., Tél, T., de Moura, APS. & Grebogi, C. (2007). 'Signatures of fractal clustering of aerosols advected under gravity'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 75, no. 6.
    [Online] DOI: 10.1103/PhysRevE.75.065203
  • Romano Blasco, MC., Thiel, M., Kurths, J. & Grebogi, C. (2007). 'Estimation of the direction of the coupling by conditional probabilities of recurrence'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 76.
    [Online] DOI: 10.1103/PhysRevE.76.036211
  • Grebogi, C., Macau, EEN. & Donato, P. (2006). 'Phase Locking Control in the Circle Map'. Nonlinear Dynamics.
  • Baptista, MS., Grebogi, C. & Koberle, R. (2006). 'Dynamically Multilayered Visual System of the Multifractal Fly'. Physical Review Letters, vol 97, no. 17.
    [Online] DOI: 10.1103/PhysRevLett.97.178102
  • Grebogi, C. & Macau, EEN. (2006). 'Control of Chaos and Its Relevancy to Spacecraft Steering'. Philosophical Transactions of the Royal Society of London. Series A, vol 364, no. 1846, pp. 2463-2481.
    [Online] DOI: 10.1098/RSTA.2006.1835
  • Vilela, RD., Moura, APS. & Grebogi, C. (2006). 'Finite-size Effects on Open Chaotic Advection'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 73.
  • Cao, Q., Wiercigroch, M., Pavlovskaia, EE., Grebogi, C. & Thompson, JMT. (2006). 'Archetypal oscillator for smooth and discontinuous dynamics'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 74, no. 4.
    [Online] DOI: 10.1103/PhysRevE.74.046218
  • Grebogi, C., Kurths, J., Gellert, M., Witt, A. & Feudel, F. (2005). 'Intersections of Stable and Unstable Manifolds: the Skeleton of Lagrangian Chaos'. Chaos, Solitons & Fractals, vol 24, pp. 947-956.
    [Online] DOI: 10.1016/j.chaos.2004.09.059
  • Grebogi, C., Viana, RL., Barbosa, JRR., Batista, AM. & Braz, EM. (2005). 'Simulating a Chaotic Process'. Brazilian Journal of Physics, vol 35, pp. 139-147.
  • Baptista, MS., Kraut, S. & Grebogi, C. (2005). 'Poincare Recurrence and Measure of Hyperbolic and Nonhyperbolic Chaotic Attractors'. Physical Review Letters, vol 95, no. 9, pp. 094101-1 - 094101-4.
    [Online] DOI: 10.1103/PhysRevLett.95.094101
  • Grebogi, C., Dzyubak, L. & Awrejcewicz, J. (2005). 'Estimation of Chaotic and Regular (Stick-slip and Slip-slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction'. Nonlinear Dynamics, vol 42, pp. 383-394.
    [Online] DOI: 10.1007/s11071-005-7183-0
  • Grebogi, C., Macau, EEN. & Freitas, US. (2005). 'Using Geometric Control and Chaotic Synchronization to Estimate an Unknown Model Parameter'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 71.
  • Tel, T., Moura, APS., Grebogi, C. & Karolyi, G. (2005). 'Chemical and Biological Activity in Open Flows: A Dynamical System Approach'. Physics Reports, vol 413, no. 2-3, pp. 91-196.
    [Online] DOI: 10.1016/J.PHYSREP.2005.01.005
  • Grebogi, C., Viana, RL., Pinto, SES., Lopes, SR., Batista, AM. & Kurths, J. (2005). 'Bubbling Bifurcation: Loss of Synchronization and Shadowing Breakdown in Complex Systems'. Physics Review D, vol 206, pp. 94-108.
    [Online] DOI: 10.1016/j.physd.2005.05.001
  • Motter, AE., Moura, APS., Grebogi, C. & Kantz, H. (2005). 'Effective Dynamics in Hamiltonian Systems with Mixed Phase Space'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 71.
  • Kraut, S. & Grebogi, C. (2004). 'Stability Properties of Nohyperbolic Chaotic Attractors with Respect to Noise'. Physical Review Letters, vol 93.
    [Online] DOI: 10.1103/PhysRevLett.93.250603
  • Grebogi, C., Dzyubak, L. & Awrejcewicz, J. (2004). 'A Direct Numerical Method for Quantifying Regular and Chaotic Orbits'. Chaos, Solitons & Fractals, vol 19, pp. 503-507.
    [Online] DOI: 10.1016/S0960-0779(03)00062-6
  • Grebogi, C., Viana, RL. & Freitas, MST. (2004). 'Basins of Attraction of Periodic Oscillations in Suspension Bridges'. Nonlinear Dynamics, vol 37, pp. 207-226.
  • Grebogi, C., Viana, RL. & Barbosa, JRR. (2004). 'Unstable Dimension Variability and Codimension-one Bifurcations of Two-dimensional Maps'. Physics Letters A, vol 321, pp. 244-251.
    [Online] DOI: 10.1016/j.physleta.2003.12.049
  • Moura, APS. & Grebogi, C. (2004). 'Chemical and Biological Activity in 3-dimensional Flows'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 70.
  • Grebogi, C. & Macau, EEN. (2004). 'Nonhyperbolic Chaotic Systems and Synchronization'. Advanced Space Dynamics, vol 4, pp. 123-132.
  • Grebogi, C., Toroczkai, Z., Motter, AE., Nishikawa, T. & Tel, T. (2004). 'Universality in Active Chaos'. Chaos, vol 14, pp. 72-78.
    [Online] DOI: 10.1063/1.1626391
  • Moura, APS. & Grebogi, C. (2004). 'Reactions in Flows with Nonhyperbolic Dynamics'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 70.
  • Grebogi, C., Viana, RL. & Freitas, MST. (2004). 'Multistability, Basin Boundary Structure, and Chaotic Behavior in a Suspension Bridge Model'. International Journal of Bifurcation and Chaos, vol 14, pp. 927-950.
  • Grebogi, C. & Kraut, S. (2004). 'Escaping from Nonhyperbolic Chaotic Attractors'. Physical Review Letters, vol 92.
  • Pavlovskaia, EE., Wiercigroch, M. & Grebogi, C. (2004). 'Two-dimensional map for impact oscillator with drift'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 70, no. 3, pp. 036201-036210.
    [Online] DOI: 10.1103/PhysRevE.70.036201
  • Grebogi, C., Baptista, MS. & Macau, EEN. (2004). 'Integrated Chaos-based Communication'. Acta Astronautica, vol 54, no. 3, pp. 153-157.
    [Online] DOI: 10.1016/S0094-5765(02)00299-0
  • Karolyi, G., Tel, T., Moura, APS. & Grebogi, C. (2004). 'Reactive Particles in Random Flows'. Physical Review Letters, vol 92, no. 17, pp. 174101-1-174101-4.
    [Online] DOI: 10.1103/PHYSREVLETT.92.174101
  • Grebogi, C., Baptista, MS. & Machado, RF. (2004). 'Cryptography with Chaos at the Physical Level'. Chaos, Solitons & Fractals, vol 21, pp. 1265-1269.
    [Online] DOI: 10.1016/j.chaos.2003.12.094
  • Grebogi, C., Macau, EEN. & Baptista, MS. (2003). 'Conditions for Efficient Chaos-based Communication'. Chaos, vol 13, pp. 145-150.
    [Online] DOI: 10.1063/1.1513061
  • Grebogi, C., Viana, RL., Pinto, SES. & Barbosa, JRR. (2003). 'Pseudo-deterministic Chaotic Systems'. International Journal of Bifurcation and Chaos, vol 13, pp. 3235-3253.
  • Grebogi, C., Kurths, J., Boccaletti, C. & Lai, YC. (2003). 'Introduction: Control and Synchronization in Chaotic Dynamical Systems'. Chaos, vol 13, pp. 126-127.
    [Online] DOI: 10.1063/1.1554606
  • Moura, APS., Motter, AE. & Grebogi, C. (2003). 'Searching in Small-world Networks'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 68, no. 3, pp. 1-5.
    [Online] DOI: 10.1103/PHYSREVE.68.036106
  • Grebogi, C., Viana, RL., Pinto, SES., Lopes, SR., Batista, AM. & Kurths, J. (2003). 'Validity of Numerical Trajectories in the Synchronization Transition of Complex Systems'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 68, no. 6, pp. 067204-1-067204-4.
    [Online] DOI: 10.1103/PHYSREVE.68.067204
  • Grebogi, C., Baptista, MS. & Barreto, E. (2003). 'Topology of Windows in High-dimensional Parameter Space Chaotic Maps'. International Journal of Bifurcation and Chaos, vol 13, pp. 2681-2688.
  • Grebogi, C., Rosa, E., Sartorelli, JC., Reyes, MB. & Baptista, MS. (2003). 'Communication-based on Topology Preservation of Chaotic Dynamics'. International Journal of Bifurcation and Chaos, vol 13, pp. 2551-2560.
  • Grebogi, C., Kapitaniak, T. & Maistrenko, Y. (2003). 'Bubbling and Riddling of Higher-dimensional Attractors'. Chaos, Solitons & Fractals, vol 17, pp. 61-66.
  • Motter, AE., Lai, YC., Grebogi, C. & Lai, Y. (2003). 'Reactive Dynamics of Inertial Particles in Nonhyperbolic Chaotic Flows'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 68, no. 5.
    [Online] DOI: 10.1103/PhysRevE.68.056307
  • Feudel, U. & Grebogi, C. (2003). 'Why Chaotic Attractors are rare in multi-stable systems'. Physical Review Letters, vol 91.
    [Online] DOI: 10.1103/PhysRevLett.91.134102
  • Grebogi, C., Viana, RL. & Freitas, MST. (2003). 'Erosion of the Safe Basin for the Transversal Oscillations of a Suspension Bridge'. Chaos, Solitons & Fractals, vol 18, pp. 829-841.
    [Online] DOI: 10.1016/S0960-0779(03)00035-3
  • Moura, APS. & Grebogi, C. (2002). 'Rainbow Transition in Chaotic Scattering'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 65, pp. 035206-1-035206-4.
    [Online] DOI: 10.1103/PHYSREVE.65.035206
  • Grebogi, C., Nishikawa, T. & Toroczkai, Z. (2002). 'Finite-size Effects on Active Chaotic Advection'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 65.
  • Grebogi, C., Kantz, H., Prasad, A., Lai, YC. & Sinde, E. (2002). 'Unexpected Robustness-against-noise of a Class of Nonhyperbolic Chaotic Attractors'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 65.
  • Grebogi, C., Viana, RL. & Pinto, SES. (2002). 'Chaotic Bursting at the Onset of Unstable Dimension Variability'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 66.
  • Macau, EEN., Grebogi, C., Lai, YC. & Lai, Y. (2002). 'Active synchronization in nonhyperbolic hyperchaotic systems'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 65, no. 2.
    [Online] DOI: 10.1103/PhysRevE.65.027202
  • Grebogi, C., Nishikawa, T., Toroczkai, Z. & Santoboni, G. (2002). 'Autocatalytic Reactions of Phase Distributed Active Particles'. Chaos, vol 12, pp. 408-412.
    [Online] DOI: 10.1063/1.1478774
  • Moura, APS. & Grebogi, C. (2002). 'Countable and Uncountable Boundaries in Chaotic Scattering'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 66.
  • Kantz, H., Grebogi, C., Prasad, A., Lai, YC., Sinde, E. & Lai, Y. (2002). 'Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 65, no. 2, pp. -.
    [Online] DOI: 10.1103/PhysRevE.65.026209
  • Grebogi, C., Valladares, DL., Boccaletti, C. & Mancini, H. (2001). 'Signal Dropout Reconstruction in Communicating with Chaos'. International Journal of Bifurcation and Chaos, vol 11, pp. 2621-2625.
  • Grebogi, C., Nishikawa, T. & Toroczkai, Z. (2001). 'Advective Coalescence in Chaotic Flows'. Physical Review Letters, vol 87.
  • Grebogi, C., Robert, C. & Aziz-Alaoui, MA. (2001). 'Dynamics of an Henon-Lozi Type Map'. Chaos, Solitons & Fractals, vol 12, pp. 2323-2341.
  • Grebogi, C., Marino, JP. & Rosa, E. (2001). 'Reconstruction of Information-bearing Chaotic Signals in Additive White Gaussian Noise: Performance Analysis and Evaluation'. International Journal of Bifurcation and Chaos, vol 11, pp. 2631-2636.
  • Grebogi, C. & Viana, RL. (2001). 'Riddled Basins and Unstable Dimension Variability in Chaotic Systems With and Without Symmetry'. International Journal of Bifurcation and Chaos, vol 11, pp. 2689-2698.
  • Moura, APS. & Grebogi, C. (2001). 'Output Functions and Fractal Dimensions in Dynamical Systems'. Physical Review Letters, vol 86, pp. 2778-2781.
  • Grebogi, C. & Macau, EEN. (2001). 'Driving Trajectories in Chaotic Systems'. International Journal of Bifurcation and Chaos, vol 11, pp. 1423-1442.
  • Pavlovskaia, EE., Wiercigroch, M. & Grebogi, C. (2001). 'Modelling of an impact system with a drift'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 64, no. 5.
    [Online] DOI: 10.1103/PhysRevE.64.056224
  • Lai, YC., de Moura, APS., Grebogi, C. & Lai, Y. (2000). 'Topology of high-dimensional chaotic scattering'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 62, no. 5, pp. 6421-6428.
    [Online] DOI: 10.1103/PhysRevE.62.6421
  • Baptista, MS., Macau, EE., Grebogi, C., Lai, YC. & Rosa, E. (2000). 'Integrated chaotic communication scheme'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 62, no. 4, pp. 4835-4845.
    [Online] DOI: 10.1103/PhysRevE.62.4835
  • Baptista, MS., Rosa, E. & Grebogi, C. (2000). 'Communication through chaotic modeling of languages'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 61, no. 4, pp. 3590-3600.
    [Online] DOI: 10.1103/PhysRevE.61.3590
  • Tonelli, R., Lai, YC., Grebogi, C. & Lai, Y. (2000). 'Feedback synchronization using pole-placement control'. International Journal of Bifurcation and Chaos, vol 10, no. 11, pp. 2611-2617.
  • Lai, YC., Grebogi, C. & Lai, Y. (2000). 'Obstruction to deterministic modeling of chaotic systems with an invariant subspace'. International Journal of Bifurcation and Chaos, vol 10, no. 3, pp. 683-693.
  • Lai, YC., Grebogi, C. & Lai, Y. (2000). 'Comment on "Riddling of chaotic sets in periodic windows" - Lai and Grebogi reply'. Physical Review Letters, vol 85, no. 2, pp. 473-473.
  • Szabo, KG., Lai, YC., Tel, T., Grebogi, C. & Lai, Y. (2000). 'Topological scaling and gap filling at crisis'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 61, no. 5, pp. 5019-5032.
  • Kapitaniak, T., Lai, YC., Grebogi, C. & Lai, Y. (1999). 'Blowout bifurcation of chaotic saddles'. Discrete dynamics in nature and society, vol 3, no. 1, pp. 9+.
  • Lai, YC., Lerner, D., Williams, K., Grebogi, C. & Lai, Y. (1999). 'Unstable dimension variability in coupled chaotic systems'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 60, no. 5, pp. 5445-5454.
  • Lai, YC., Grebogi, C. & Lai, Y. (1999). 'Riddling of chaotic sets in periodic windows'. Physical Review Letters, vol 83, no. 15, pp. 2926-2929.
  • Kapitaniak, T., Lai, YC., Grebogi, C. & Lai, Y. (1999). 'Metamorphosis of chaotic saddle'. Physics Letters A, vol 259, no. 6, pp. 445-450.
  • Lai, YC., Grebogi, C. & Lai, Y. (1999). 'Modeling of coupled chaotic oscillators'. Physical Review Letters, vol 82, no. 24, pp. 4803-4806.
  • Lai, YC., Zyczkowski, K., Grebogi, C. & Lai, Y. (1999). 'Universal behavior in the parametric evolution of chaotic saddles'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 59, no. 5, pp. 5261-5265.
  • Lai, YC., Bollt, E., Grebogi, C. & Lai, Y. (1999). 'Communicating with chaos using two-dimensional symbolic dynamics'. Physics Letters A, vol 255, no. 1-2, pp. 75-81.
  • Lai, YC., Grebogi, C., Kurths, J. & Lai, Y. (1999). 'Modeling of deterministic chaotic systems'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 59, no. 3, pp. 2907-2910.
  • Feudel, U., Witt, A., Lai, YC., Grebogi, C. & Lai, Y. (1998). 'Basin bifurcation in quasiperiodically forced systems'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 58, no. 3, pp. 3060-3066.
  • Bollt, E., Lai, YC., Grebogi, C. & Lai, Y. (1997). 'Coding, channel capacity, and noise resistance in communicating with chaos'. Physical Review Letters, vol 79, no. 19, pp. 3787-3790.
  • Grebogi, C., Lai, YC., Hayes, S. & Lai, Y. (1997). 'Control and applications of chaos'. Journal of the franklin institute-Engineering and applied mathematics, vol 334B, no. 5-6, pp. 1115-1146.
  • Grebogi, C., Lai, YC. & Lai, Y. (1997). 'Controlling chaotic dynamical systems'. Systems & control letters, vol 31, no. 5, pp. 307-312.
  • Grebogi, C., Lai, YC. & Lai, Y. (1997). 'Controlling chaos in high dimensions'. Ieee transactions on circuits and systems i-Fundamental theory and applications, vol 44, no. 10, pp. 971-975.
  • Lai, YC., Nagai, Y., Grebogi, C. & Lai, Y. (1997). 'Characterization of the natural measure by unstable periodic orbits in chaotic attractors'. Physical Review Letters, vol 79, no. 4, pp. 649-652.
  • Lai, YC., Feudel, U., Grebogi, C. & Lai, Y. (1996). 'Scaling behavior of transition to chaos in quasiperiodically driven dynamical systems'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 54, no. 6, pp. 6070-6073.
  • Lai, YC., Grebogi, C. & Lai, Y. (1996). 'Noise-induced riddling in chaotic systems'. Physical Review Letters, vol 77, no. 25, pp. 5047-5050.
  • Lai, YC., Grebogi, C. & Lai, Y. (1996). 'Complexity in Hamiltonian-driven dissipative chaotic dynamical systems'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 54, no. 5, pp. 4667-4675.
  • Szabo, KG., Lai, YC., Tel, T., Grebogi, C. & Lai, Y. (1996). 'Critical exponent for gap filling at crisis'. Physical Review Letters, vol 77, no. 15, pp. 3102-3105.
  • Lai, YC., Grebogi, C., Yorke, JA., Venkataramani, SC. & Lai, Y. (1996). 'Riddling bifurcation in chaotic dynamical systems'. Physical Review Letters, vol 77, no. 1, pp. 55-58.
  • Lai, YC., Grebogi, C. & Lai, Y. (1996). 'Characterizing riddled fractal sets'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 53, no. 2, pp. 1371-1374.
  • LAI, YC., GREBOGI., C., KOSTELICH., EJ. & Lai, Y. (1994). 'EXTREME FINAL-STATE SENSITIVITY IN INHOMOGENEOUS SPATIOTEMPORAL CHAOTIC SYSTEMS'. Physics Letters A, vol 196, no. 3-4, pp. 206-212.
  • LAI, YC., GREBOGI., C. & Lai, Y. (1994). 'SYNCHRONIZATION OF SPATIOTEMPORAL CHAOTIC SYSTEMS BY FEEDBACK-CONTROL'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 50, no. 3, pp. 1894-1899.
  • LAI, YC., GREBOGI., C. & Lai, Y. (1994). 'CRISIS AND ENHANCEMENT OF CHAOTIC SCATTERING'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 49, no. 5, pp. 3761-3770.
  • LAI, YC., GREBOGI., C. & Lai, Y. (1994). 'CONVERTING TRANSIENT CHAOS INTO SUSTAINED CHAOS BY FEEDBACK-CONTROL'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 49, no. 2, pp. 1094-1098.
  • LAI, YC., GREBOGI., C., YORKE., JA., KAN., I. & Lai, Y. (1993). 'HOW OFTEN ARE CHAOTIC SADDLES NONHYPERBOLIC'. Nonlinearity, vol 6, no. 5, pp. 779-797.
  • LAI, YC., GREBOGI., C., BLUMEL., R., KAN, I. & Lai, Y. (1993). 'CRISIS IN CHAOTIC SCATTERING'. Physical Review Letters, vol 71, no. 14, pp. 2212-2215.
  • LAI, YC., TEL., T., GREBOGI., C. & Lai, Y. (1993). 'STABILIZING CHAOTIC-SCATTERING TRAJECTORIES USING CONTROL'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 48, no. 2, pp. 709-717.
  • LAI, YC., GREBOGI., C. & Lai, Y. (1993). 'SYNCHRONIZATION OF CHAOTIC TRAJECTORIES USING CONTROL'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 47, no. 4, pp. 2357-2360.
  • LAI, YC., DING., MZ., GREBOGI., C. & Lai, Y. (1993). 'CONTROLLING HAMILTONIAN CHAOS'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 47, no. 1, pp. 86-92.
  • LAI, YC., OTT., E., GREBOGI., C. & Lai, Y. (1993). 'TEMPORAL CROSSOVER FROM CLASSICAL TO QUANTUM BEHAVIOR - A MARKOV-CHAIN APPROACH'. Physics Letters A, vol 173, no. 2, pp. 148-152.
  • LAI, YC., DING., MZ., GREBOGI., C., BLUMEL., R. & Lai, Y. (1992). 'ALGEBRAIC DECAY AND FLUCTUATIONS OF THE DECAY EXPONENT IN HAMILTONIAN-SYSTEMS'. Physical Review A, vol 46, no. 8, pp. 4661-4669.
  • LAI, YC., BLUMEL., R., OTT, E., GREBOGI., C. & Lai, Y. (1992). 'QUANTUM MANIFESTATIONS OF CHAOTIC SCATTERING'. Physical Review Letters, vol 68, no. 24, pp. 3491-3494.

Comments and Debates

  • LAI, YC., GREBOGI., C. & Lai, Y. (1995). 'INTERMINGLED BASINS AND 2-STATE ON-OFF INTERMITTENCY'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 52, no. 4, pp. R3313-R3316.
  • LAI, YC., GREBOGI., C., BLUMEL., R., DING, MZ. & Lai, Y. (1992). 'ALGEBRAIC DECAY AND PHASE-SPACE METAMORPHOSES IN MICROWAVE IONIZATION OF HYDROGEN RYDBERG ATOMS'. Physical Review A, vol 45, no. 11, pp. 8284-8287.

Scientific Reviews

  • Boccaletti, S., Grebogi, C., Lai, YC., Mancini, H., Maza, D. & Lai, Y. (2000). 'The control of chaos: theory and applications'. Physics Reports, vol 329, no. 3, pp. 103-197.
  • Grebogi, C., Lai, YC., Hayes, S. & Lai, Y. (1997). 'Control and applications of chaos'. International Journal of Bifurcation and Chaos, vol 7, no. 10, pp. 2175-2197.

Chapters in Books, Reports and Conference Proceedings

Chapters

  • de Moura, APS. & Grebogi, C. (2011). 'Nonlinear dynamics: a brief introduction'. in M Stumpf, M Girolami & D Balding (eds), Handbook of Statistical Systems Biology Wiley-Blackwell, pp. 333.
    [Online] AURA: c16_1.pdf
  • Grebogi, C., Freitas, MST. & Viana, RL. (2005). 'Multistability in Suspension Bridges'. Modelling and Control of Autonomous Decision Support System Modelling and Control of Autonomous Decision Support System, pp. 111-124.
  • Moura, APS. & Grebogi, C. (2005). 'Caos em Sistemas Dinamicos'. Fisica: Tendencias e Perspectivas Fisica: Tendencias e Perspectivas, pp. 99-107.
  • Grebogi, C., Pinto, SES., Viana, RL. & Barbosa, JRR. (2003). 'Shadowing and Modelling in Chaotic Dynamics'. Anais do I Encontro Nacional de Fisica Teorica e Computacional, Brasilia Anais do I Encontro Nacional de Fisica Teorica e Computacional, Brasilia.
  • Grebogi, C., Poon, L., Sauer, T., Yorke, JA. & Auerbach, D. (2002). 'Shadowability of Chaotic Dynamical Systems'. Handbook on Dynamical Systems: Towards Applications Handbook on Dynamical Systems: Towards Applications, pp. 313-344.
  • Grebogi, C., Barbosa, JRR., Pinto, SES. & Viana, RL. (2002). 'Shadowability: Validity of Chaotic Trajectories'. International Centre of Condensed Matter Physics Publication International Centre of Condensed Matter Physics Publication.
  • Grebogi, C., Viana, RL. & Pinto, SES. (2002). 'Obstruction to Modelling and Shadowing'. Fifth World Congress on Computational Mechanics Fifth World Congress on Computational Mechanics.
  • Grebogi, C., Rosa, E., Boccaletti, C., Valadares, DL. & Marino, IP. (2001). 'Communication With Chaos: Reconstructing Information-carrying Signals'. Space-time Chaos: Characterization, Control, and Synchronization Space-time Chaos: Characterization, Control, and Synchronization, pp. 273-291.

Conference Proceedings

  • Baptista, MS., Hunt, BR., Grebogi, C., Ott, E. & Yorke, JA. (2000). 'Control of shipboard cranes'. in N Van Dao & EJ Kreuzer (eds), IUTAM Symposium on Recent Developments in Non-Linear Oscillations of Mechanical Systems vol. 77, Solid Mechanics and Its Applications, Kluwer Academic Publishers, London, England, pp. 75-84.
  • Lai, YC., Grebogi, C. & Lai, Y. (2000). 'Necessity of statistical modeling of deterministic chaotic systems'. in M Tokuyama & H Stanley (eds), STATISTICAL PHYSICS AMER INST PHYSICS, MELVILLE, pp. 531-542, 3rd Tohwa University International Conference on Statistical Physics, FUKUOKA, 9/11/99.
  • Grebogi, C., Lai, YC., Hayes, S. & Lai, Y. (1996). 'Chaos: Control and communication'. in N Abraham & Y Khanin (eds), NONLINEAR DYNAMICS IN LASERS SPIE - INT SOC OPTICAL ENGINEERING, BELLINGHAM, pp. 15-29, Symposium on Nonlinear Dynamics in Lasers, at the 8th Laser Optics Conference, ST PETERSBURG, 27/06/95.
  • GREBOGI, C., LAI., YC. & Lai, Y. (1994). 'CONTROL AND USE OF CHAOS'. in J Thompson & S Bishop (eds), NONLINEARITY AND CHAOS IN ENGINEERING DYNAMICS John Wiley & Sons Ltd, CHICHESTER, pp. 393-402, Symposium on Nonlinearity and Chaos in Engineering Dynamics, LONDON, 19/07/93.
  • LAI, YC., GREBOGI., C., TEL., T. & Lai, Y. (1994). 'CONTROLLING TRANSIENT CHAOS IN DYNAMICAL SYSTEMS'. in M Yamaguti (ed.), TOWARDS THE HARNESSING OF CHAOS ELSEVIER SCIENCE PUBL B V, AMSTERDAM, pp. 153-167, 7th TOYOTA Conference - Towards the Harnessing of Chaos, MIKKABI, 31/10/93.
  • LAI, YC., GREBOGI., C. & Lai, Y. (1993). 'SYNCHRONIZATION OF A CHAOTIC OPTICAL-SYSTEM USING CONTROL'. in L Pecora (ed.), CHAOS IN COMMUNICATIONS SPIE - INT SOC OPTICAL ENGINEERING, BELLINGHAM, pp. 91-102, Conference on Chaos in Communications, SAN DIEGO, 14/07/93.
  • LAI, YC., DING., MZ., GREBOGI., C. & Lai, Y. (1993). 'CONTROLLING CHAOS IN HAMILTONIAN-SYSTEMS'. in P Christiansen, J Eilbeck & R Parmentier (eds), FUTURE DIRECTIONS OF NONLINEAR DYNAMICS IN PHYSICAL AND BIOLOGICAL SYSTEMS PLENUM PRESS DIV PLENUM PUBLISHING CORP, NEW YORK, pp. 129-137, NATO Advanced Study Institute on Future Directions of Nonlinear Dynamics in Physical and Biological Systems, in honor of Alwyn Scotts 60th Birthday, LYNGBY, 23/07/92.
  • LAI, YC., GREBOGI., C., YORKE., JA. & Lai, Y. (1992). 'SUDDEN CHANGE IN THE SIZE OF CHAOTIC ATTRACTORS - HOW DOES IT OCCUR'. in J Kim & J Stringer (eds), APPLIED CHAOS JOHN WILEY & SONS INC, NEW YORK, pp. 441-455, INTERNATIONAL WORKSHOP ON APPLICATIONS OF CHAOS, SAN FRANCISCO, 4/12/90.

Contributions to Conferences

Other Contributions

  • Moura, APS. & Grebogi, C. (2004). 'Three-dimensional Effects in Active Chaotic Flows'.

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