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The School of Natural and Computing Sciences

Professor Celso Grebogi

Professor Celso Grebogi
Professor Celso Grebogi
Professor Celso Grebogi

CEng, MS, PhD, Drhc-mult, FRSE, FTWAS, MAE, FABC, FAPS, FInstP

Sixth Century Chair in Nonlinear & Complex Systems

About
Email Address
grebogi@abdn.ac.uk
Telephone Number
+44 (0)1224 272791
Office Address

Institute for Complex Systems and Mathematical Biology

King's College, University of Aberdeen

Old Aberdeen AB24 3UE, UK

School/Department
School of Natural and Computing Sciences
ORCiD
Google Scholar
Pure
Personal Website

Biography

Professor Celso Grebogi is the Sixth Century Chair at King’s College, University of Aberdeen, UK. He is the Founding Director of the Institute for Complex Systems and Mathematical Biology, whose work in systems biology and complex systems became leading in UK. He is the Co-founder of the Aberdeen-Lanzhou-Tempe Research Centre, whose work is in the new interdisciplinary field: Relativistic Quantum Chaos. He has been an External Scientific Member (Mitglied) of the Max-Planck-Society since 1998. He got his PhD in Theoretical Physics from the University of Maryland in 1978, Postdoc in Physics and Applied Mathematics at UC Berkeley in 1978-1981. He was at the University of Sao Paulo as Professor of Physics, and, before that, with the University of Maryland as Professor of Mathematics. He is a leading expert in chaotic and complex nonlinear dynamics, including fractal geometry and complex networks. He has made a huge impact in the area of control of chaos. His seminal paper was selected by Physical Review Letters as a milestone in the past 50 years. He was awarded the Citation Laureate - Researcher of Nobel Class - in 2016, followed by a Motion to that effect supported by the Scottish Parliament. His scientific accomplishments include over 500 publications and over 500 invited talks. He received numerous distinctions, including multiple Doctor Honoris Causa and many Honorary Professorships, the Humboldt Senior Prize, Fulbright Fellowship, and Toshiba Chair as a World-renown Scholar, the Lagrange Award, the Max-Planck-Society Badge of Honour, and the James Yorke Award. He is Fellow in various scientific societies, including the Royal Society of Edinburgh, The World Academy of Sciences, the Academia Europaea, the Brazilian Academy of Sciences, The American Physical Society and the UK Institute of Physics. He has 32,000 citations and h-index = 84 in Scopus, and 47,000 citations and h-index = 96 in Google Scholar.

 

Memberships and Affiliations

Internal Memberships

 

  • BSc, 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
  • External Scientific Member (Mitglied), Max-Planck-Society, since 1998
  • Professeur Invité, Université du Le Havre Normandie, 2001
  • Professor Titular, University of Sao Paulo, 2001-2005
  • Sixth Century Chair in Nonlinear and Complex Systems, University of Aberdeen, since 2005
  • Director of the Nonlinear Dynamics and Complex Systems Group. The Northern Research Partnership of Scottish Universities, 2007-2010
  • Founding Director of the Institute for Complex Systems and Mathematical Biology, since 2009
  • Visiting Professor, Institute of Medical Engineering, Xi'an Jiaotong University, 2010-2013
  • Senior Fellow of the Freiburg Institute for Advanced Studies, 2011-2013
  • Co-founder of the Aberdeen-Lanzhou-Tempe Joint Research Centre for Computation and Complexity, 2012
  • Visiting Professor, Xi'an University of Technology, since 2017

 

External Memberships

 

  • Fellow of the American Physical Society, 1991
  • Fellow of the Brazilian Academy of Sciences, 2003
  • Fellow of The World Academy of Sciences (TWAS/UNESCO), 2004
  • Fellow of the Institute of Physics (UK), 2011
  • Fellow of the Royal Society of Edinburgh, 2012
  • Member of the Academia Europaea, 2019
  • External Scientific Member (Mitglied), Max-Planck-Society, since 1998
  • Honorary Member of the International Physics and Control Society, 2009
  • Member of over a two dozen Editorial Boards and Associate Editorships over the years
  • Membership in various scientific societies

 

 

Prizes and Awards

 

  • Fulbright Fellowship Award, 1974
  • Distinguished Scientist Lecturer, Carnegie Mellon University, 1989
  • Toshiba Chair as World-renowned Scholar, 1995
  • Awarded the 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, Germany, 1997
  • Humboldt Prize Revisited Award, 2003
  • Controlling Chaos, Physical Review Letters selected it as a milestone  in the past 50 years, 2008
  • Honorary Professorship, Xi'an University of Technology, China, 2012
  • Honorary Pofessorship, Lanzhou University, China, 2012
  • Doctor Honoris Causa, Le Havre Normandie University, France, 2014
  • Honorary Professorship, Xi'an Jiaotong University, China, 2015
  • Awarded the Citation Laureate - Researcher of Nobel Class, 2016
  • Motion S5M-01678 supported in the Scottish Parliament: "Aberdeen Academic Included in Citation Laureate", 27/09/2016
  • Honorary Professorship, Tianjin University, China, 2018
  • Honorary Expert, Weifang/Weicheng City, Shandong, China, 2018
  • Honorary Professorship, Huaqiao Unviversity, China, 2018
  • Honorary Expert, National Institute of Metrology, Yantai, China, 2019
  • Burgess of Guild, The Burgesses of Guild of the City and Royal Burgh of Aberdeen, Scotland, 2022
  • Badge of Honour from the President of the Max-Planck-Society, 22 June 2023
  • Lagrange Award for Lifetime Achievement in Nonlinear Physical Science, 10 July 2023
  • James Yorke Award for for breakthrough achievements in Nonlinear Dynamics and Chaos, 22 June 2024
  • Scopus: 32,000 citations in indexed journals, h-index = 84
  • Google Scholar: 47,000 citations, h-index = 96

 

Research

Research Overview

Dynamics of nonlinear and complex systems including chaotic dynamics, fractal geometry, systems biology, population dynamics, neurodynamics, fluid advection, relativistic quantum nonlinear dynamics, and nanosystems.

Publications

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  • Finite-size particles, advection, and chaos: A collective phenomenon of intermittent bursting (vol 78, art no 056206, 2008): Publisher's Note

    Medrano-T, R. O., Moura, A., Tel, T., Caldas, I. L., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 78, no. 6, 069901
    Contributions to Journals: Articles

  • Finite-size particles, advection, and chaos: a collective phenomenon of intermittent bursting

    Medrano-T, R. O., Moura, A. P. S., Tel, T., Caldas, I. L., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 78, no. 5, 056206
    Contributions to Journals: Articles

  • Transition to chaotic scattering: Signatures in the differential cross section

    Schelin, A., de Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 78, no. 4 , 046204
    Contributions to Journals: Articles

  • Crisis-induced unstable dimension variability in a dynamical system

    Kubo, G. T., Viana, R. L., Lopes, S. R., Grebogi, C.
    Physics Letters A, vol. 372, no. 34, pp. 5569-5574
    Contributions to Journals: Articles

  • The limit case response of archetypal oscillator for smooth and discontinuous dynamics

    Cao, Q., Wiercigroch, M., Pavlovskaia, E. E., Grebogi, C., Thompson, J. M. T.
    International Journal of Non-Linear Mechanics, vol. 43, no. 6, pp. 462-473
    Contributions to Journals: Articles

  • International Journal of Bifurcation and Chaos: Editorial

    Pisarchik, A. N., Grebogi, C.
    International Journal of Bifurcation and Chaos, vol. 18, no. 6, pp. 1605-1606
    Contributions to Journals: Editorials

  • Experimental chaos II - Preface

    Macau, E. E. N., Grebogi, C., Kurths, J.
    Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, vol. 366, no. 1865, pp. 489-491
    Contributions to Journals: Editorials

  • Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics

    Cao, Q., Wiercigroch, M., Pavlovskaia, E. E., Thompson, J. M. T., Grebogi, C.
    Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, vol. 366, no. 1865, pp. 635-652
    Contributions to Journals: Articles

  • A complex biological system: the fly's visual module

    Baptista, M. S., de Almeida, L. O. B., Slaets, J. F. W., Koberle, R., Grebogi, C.
    Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, vol. 366, no. 1864, pp. 345-357
    Contributions to Journals: Articles

  • Experimental chaos I - Preface

    Macau, E. E. N., Grebogi, C., Kurths, J.
    Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, vol. 366, no. 1864, pp. 315-317
    Contributions to Journals: Editorials

  • Controlling Chaos

    Macau, E. E. N., Grebogi, C.
    Handbook of Chaos Control. Scholl, E., Schuster, H. G. (eds.). 2 edition. Wiley-VCH, pp. 1-28, 28 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Onset of chaotic advection in open flows

    Biemond, J. J. B., Moura, A. P. S., Karolyi, G., Grebogi, C., Nijmeijer, H.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 78, no. 1, 016317
    Contributions to Journals: Articles

  • The SD Oscillator and Its Attractors

    Cao, Q., Wiercigroch, M., Pavlovskaia, E., Grebogi, C., Michael, J., Thompson, T.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Untitled

    Pisarchik, A. N., Grebogi, C.
    International Journal of Bifurcation and Chaos, vol. 18, pp. 1605-1606
    Contributions to Journals: Editorials

  • SD oscillator, the attractor and their applications

    Cao, Q. J., Wiercigroch, M., Pavlovskaia, E. E., Grebogi, C., Thompson, J. M. T.
    Zhendong Gongcheng Xuebao/Journal of Vibration Engineering, vol. 20, no. 5, pp. 454-458
    Contributions to Journals: Articles

  • Estimation of the direction of the coupling by conditional probabilities of recurrence

    Romano, M. C., Thiel, M., Kurths, J., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 76, no. 3, 036211
    Contributions to Journals: Articles

  • Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation

    Pereira, R. F., Pinto, S. E. d. S., Viana, R. L., Lopes, S. R., Grebogi, C.
    Chaos, vol. 17, no. 2, 023131
    Contributions to Journals: Articles

  • Signatures of fractal clustering of aerosols advected under gravity

    Vilela, R. D., Tél, T., de Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 75, no. 6, 065203(R)
    Contributions to Journals: Articles

  • Phase locking control in the Circle Map

    Almeida Di Donato, P. F., Macau, E. E. N., Grebogi, C.
    Nonlinear Dynamics, vol. 47, no. 1-3, pp. 75-82
    Contributions to Journals: Articles

  • Chaotic advection and fractality: applications in oceanography

    Karolyi, G., Grebogi, C.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Archetypal oscillator for smooth and discontinuous dynamics

    Cao, Q., Wiercigroch, M., Pavlovskaia, E. E., Grebogi, C., Thompson, J. M. T.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 74, no. 4, 046218
    Contributions to Journals: Articles

  • Dynamically Multilayered Visual System of the Multifractal Fly

    Baptista, M. S., Grebogi, C., Koberle, R.
    Physical Review Letters, vol. 97, no. 17
    Contributions to Journals: Articles

  • Control of Chaos and Its Relevancy to Spacecraft Steering

    Grebogi, C., Macau, E. E. N.
    Philosophical Transactions of the Royal Society of London. Series A, vol. 364, no. 1846, pp. 2463-2481
    Contributions to Journals: Articles

  • Finite-size effects on open chaotic advection

    Vilela, R. D., de Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 73, no. 2, 026302
    Contributions to Journals: Articles

  • Poincare Recurrence and Measure of Hyperbolic and Nonhyperbolic Chaotic Attractors

    Baptista, M. S., Kraut, S., Grebogi, C.
    Physical Review Letters, vol. 95, no. 9, pp. 094101-1 - 094101-4
    Contributions to Journals: Articles

  • Chemical and biological activity in open flows: a dynamical system approach (vol 413, pg 91, 2005)

    Tel, T., de Moura, A., Grebogi, C., Karolyi, G.
    Physics Reports, vol. 415, no. 5-6, pp. 360-360
    Contributions to Journals: Articles

  • Chemical and Biological Activity in Open Flows: A Dynamical System Approach

    Tel, T., Moura, A. P. S., Grebogi, C., Karolyi, G.
    Physics Reports, vol. 413, no. 2-3, pp. 91-196
    Contributions to Journals: Articles

  • Using geometric control and chaotic synchronization to estimate an unknown model parameter

    Freitas, U. S., Macau, E. E. N., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 71, no. 4, 047203
    Contributions to Journals: Articles

  • Effective Dynamics in Hamiltonian Systems with Mixed Phase Space

    Motter, A. E., de Moura, A. P. S., Grebogi, C., Kantz, H.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 71, no. 3, 036215
    Contributions to Journals: Articles

  • Bubbling Bifurcation: Loss of Synchronization and Shadowing Breakdown in Complex Systems

    Grebogi, C., Viana, R. L., Pinto, S. E. S., Lopes, S. R., Batista, A. M., Kurths, J.
    Physics Review D, vol. 206, pp. 94-108
    Contributions to Journals: Articles

  • Caos em Sistemas Dinamicos

    Moura, A. P. S., Grebogi, C.
    Fisica: Tendencias e Perspectivas, pp. 99-107, 8 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Estimation of Chaotic and Regular (Stick-slip and Slip-slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction

    Grebogi, C., Dzyubak, L., Awrejcewicz, J.
    Nonlinear Dynamics, vol. 42, pp. 383-394
    Contributions to Journals: Articles

  • Intersections of Stable and Unstable Manifolds: the Skeleton of Lagrangian Chaos

    Grebogi, C., Kurths, J., Gellert, M., Witt, A., Feudel, F.
    Chaos, Solitons & Fractals, vol. 24, pp. 947-956
    Contributions to Journals: Articles

  • Multistability in Suspension Bridges

    Grebogi, C., Freitas, M. S. T., Viana, R. L.
    Modelling and Control of Autonomous Decision Support System, pp. 111-124, 13 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Simulating a Chaotic Process

    Grebogi, C., Viana, R. L., Barbosa, J. R. R., Batista, A. M., Braz, E. M.
    Brazilian Journal of Physics, vol. 35, pp. 139-147
    Contributions to Journals: Articles

  • Stability properties of nonhyperbolic chaotic attractors with respect to noise

    Kraut, S., Grebogi, C.
    Physical Review Letters, vol. 93, no. 25, 250603
    Contributions to Journals: Articles

  • Reactions in Flows with Nonhyperbolic Dynamics

    de Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 70, no. 3, 036216
    Contributions to Journals: Articles

  • Two-dimensional map for impact oscillator with drift

    Pavlovskaia, E. E., Wiercigroch, M., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 70, no. 3, pp. 036201-036210
    Contributions to Journals: Articles

  • Chemical and biological activity in three-dimensional flows

    de Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 70, no. 2, 026218
    Contributions to Journals: Articles

  • Escaping from nonhyperbolic chaotic attractors

    Kraut, S., Grebogi, C.
    Physical Review Letters, vol. 92, no. 23, 234101
    Contributions to Journals: Articles

  • Surfando no Caos

    Macau, E. E., Grebogi, C.
    Ciência Hoje , vol. 34, pp. 20-27
    Contributions to Journals: Articles

  • Reactive particles in random flows

    Karolyi, G., Tel, T., de Moura, A. P. S., Grebogi, C.
    Physical Review Letters, vol. 92, no. 17, 174101
    Contributions to Journals: Articles

  • Integrated Chaos-based Communication

    Grebogi, C., Baptista, M. S., Macau, E. E. N.
    Acta Astronautica, vol. 54, no. 3, pp. 153-157
    Contributions to Journals: Articles

  • A Direct Numerical Method for Quantifying Regular and Chaotic Orbits,

    Grebogi, C., Dzyubak, L., Awrejcewicz, J.
    Chaos, Solitons & Fractals, vol. 19, pp. 503-507
    Contributions to Journals: Articles

  • Basins of Attraction of Periodic Oscillations in Suspension Bridges

    Grebogi, C., Viana, R. L., Freitas, M. S. T.
    Nonlinear Dynamics, vol. 37, pp. 207-226
    Contributions to Journals: Articles

  • Chemical and Biological Activity in 3-dimensional Flows

    Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 70
    Contributions to Journals: Articles

  • Cryptography with Chaos at the Physical Level

    Grebogi, C., Baptista, M. S., Machado, R. F.
    Chaos, Solitons & Fractals, vol. 21, pp. 1265-1269
    Contributions to Journals: Articles

  • Multistability, Basin Boundary Structure, and Chaotic Behavior in a Suspension Bridge Model

    Grebogi, C., Viana, R. L., Freitas, M. S. T.
    International Journal of Bifurcation and Chaos, vol. 14, pp. 927-950
    Contributions to Journals: Articles

  • Nonhyperbolic Chaotic Systems and Synchronization

    Grebogi, C., Macau, E. E. N.
    Advanced Space Dynamics, vol. 4, pp. 123-132
    Contributions to Journals: Articles

  • Three-dimensional Effects in Active Chaotic Flows

    Moura, A. P. S., Grebogi, C.
    Contributions to Conferences: Other Contributions

  • Three-dimensional effects in active chaotic flows

    de Moura, A. P. S., Grebogi, C.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Universality in Active Chaos

    Grebogi, C., Toroczkai, Z., Motter, A. E., Nishikawa, T., Tel, T.
    Chaos, vol. 14, pp. 72-78
    Contributions to Journals: Articles

  • Unstable Dimension Variability and Codimension-one Bifurcations of Two-dimensional Maps

    Grebogi, C., Viana, R. L., Barbosa, J. R. R.
    Physics Letters A, vol. 321, pp. 244-251
    Contributions to Journals: Articles

  • Validity of Numerical Trajectories in the Synchronization Transition of Complex Systems

    Viana, R. L., Grebogi, C., Pinto, S. E. D. S., Lopes, S. R., Batista, A. M., Kurths, J.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 68, no. 6, 067204
    Contributions to Journals: Articles

  • Reactive Dynamics of Inertial Particles in Nonhyperbolic Chaotic Flows

    Motter, A. E., Lai, Y. C., Grebogi, C., Lai, Y.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 68, no. 5, 056307
    Contributions to Journals: Articles

  • Why are chaotic attractors rare in multistable systems?

    Feudel, U., Grebogi, C.
    Physical Review Letters, vol. 91, no. 13, 134102
    Contributions to Journals: Articles

  • Searching in small-world networks

    de Moura, A. P. S., Motter, A. E., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 68, no. 3, 036106
    Contributions to Journals: Articles

  • Topology of windows in the high-dimensional parameter space of chaotic maps

    Baptista, M. S., Grebogi, C., Barreto, E.
    International Journal of Bifurcation and Chaos, vol. 13, no. 9, pp. 2681-2688
    Contributions to Journals: Articles

  • Bubbling and Riddling of Higher-dimensional Attractors

    Grebogi, C., Kapitaniak, T., Maistrenko, Y.
    Chaos, Solitons & Fractals, vol. 17, pp. 61-66
    Contributions to Journals: Articles

  • Communication-based on Topology Preservation of Chaotic Dynamics

    Grebogi, C., Rosa, E., Sartorelli, J. C., Reyes, M. B., Baptista, M. S.
    International Journal of Bifurcation and Chaos, vol. 13, pp. 2551-2560
    Contributions to Journals: Articles

  • Conditions for Efficient Chaos-based Communication

    Grebogi, C., Macau, E. E. N., Baptista, M. S.
    Chaos, vol. 13, pp. 145-150
    Contributions to Journals: Articles

  • Erosion of the Safe Basin for the Transversal Oscillations of a Suspension Bridge

    Grebogi, C., Viana, R. L., Freitas, M. S. T.
    Chaos, Solitons & Fractals, vol. 18, pp. 829-841
    Contributions to Journals: Articles

  • Foreword to Chaotic Signals in Digital Communications

    Grebogi, C., Ren, H.
    Chaotic Signals in Digital Communications. Eisencraft, M., Attux, R., Suyama, R. (eds.). CRC Press, pp. xxvii-xxviii, 2 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Introduction: Control and Synchronization in Chaotic Dynamical Systems

    Grebogi, C., Kurths, J., Boccaletti, C., Lai, Y. C.
    Chaos, vol. 13, pp. 126-127
    Contributions to Journals: Articles

  • Pseudo-deterministic Chaotic Systems

    Grebogi, C., Viana, R. L., Pinto, S. E. S., Barbosa, J. R. R.
    International Journal of Bifurcation and Chaos, vol. 13, pp. 3235-3253
    Contributions to Journals: Articles

  • Shadowing and Modelling in Chaotic Dynamics

    Grebogi, C., Pinto, S. E. S., Viana, R. L., Barbosa, J. R. R.
    Anais do I Encontro Nacional de Fisica Teorica e Computacional, Brasilia
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Topology of Windows in High-dimensional Parameter Space Chaotic Maps

    Grebogi, C., Baptista, M. S., Barreto, E.
    International Journal of Bifurcation and Chaos, vol. 13, pp. 2681-2688
    Contributions to Journals: Articles

  • Chaotic bursting at the onset of unstable dimension variability

    Viana, R. L., Pinto, S. E. D., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 66, no. 4, 046213
    Contributions to Journals: Articles

  • Countable and Uncountable Boundaries in Chaotic Scattering

    de Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 66, no. 4, 046214
    Contributions to Journals: Articles

  • Rainbow Transition in Chaotic Scattering

    de Moura, A. P. S., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 65, no. 3, 035206
    Contributions to Journals: Articles

  • Active synchronization in nonhyperbolic hyperchaotic systems

    Macau, E. E. N., Grebogi, C., Lai, Y. C., Lai, Y.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 65, no. 2, 027202
    Contributions to Journals: Articles

  • Finite-size Effects on Active Chaotic Advection

    Nishikawa, T., Toroczkai, Z., Grebogi, C., Tel, T.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 65, no. 2, 026216
    Contributions to Journals: Articles

  • Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors

    Kantz, H., Grebogi, C., Prasad, A., Lai, Y., Sinde, E.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 65, no. 2, 026209
    Contributions to Journals: Articles

  • Autocatalytic Reactions of Phase Distributed Active Particles

    Grebogi, C., Nishikawa, T., Toroczkai, Z., Santoboni, G.
    Chaos, vol. 12, pp. 408-412
    Contributions to Journals: Articles

  • Obstruction to Modelling and Shadowing

    Grebogi, C., Viana, R. L., Pinto, S. E. S.
    Fifth World Congress on Computational Mechanics
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Shadowability of Chaotic Dynamical Systems

    Grebogi, C., Poon, L., Sauer, T., Yorke, J. A., Auerbach, D.
    Handbook on Dynamical Systems: Towards Applications, pp. 313-344, 31 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Shadowability: Validity of Chaotic Trajectories

    Grebogi, C., Barbosa, J. R. R., Pinto, S. E. S., Viana, R. L.
    International Centre of Condensed Matter Physics Publication
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Modeling of an impact system with a drift

    Pavlovskaia, E., Wiercigroch, M., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 64, no. 5, 056224
    Contributions to Journals: Articles

  • Advective Coalescence in Chaotic Flows

    Nishikawa, T., Toroczkai, Z., Grebogi, C.
    Physical Review Letters, vol. 87, no. 3, 038301
    Contributions to Journals: Articles

  • Bifurcations in Piecewise Smooth Maps

    Banerjee, S., Grebogi, C.
    Nonlinear Phenomena in Power Electronics: Bifurcations, Chaos, Control, and Applications. Banerjee, S., Verghese, G. C. (eds.). IEEE Press
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Communication With Chaos: Reconstructing Information-carrying Signals

    Grebogi, C., Rosa, E., Boccaletti, C., Valadares, D. L., Marino, I. P.
    Space-time Chaos: Characterization, Control, and Synchronization, pp. 273-291, 18 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Driving Trajectories in Chaotic Systems

    Grebogi, C., Macau, E. E. N.
    International Journal of Bifurcation and Chaos, vol. 11, pp. 1423-1442
    Contributions to Journals: Articles

  • Dynamics of an Henon-Lozi Type Map

    Grebogi, C., Robert, C., Aziz-Alaoui, M. A.
    Chaos, Solitons & Fractals, vol. 12, pp. 2323-2341
    Contributions to Journals: Articles

  • Output Functions and Fractal Dimensions in Dynamical Systems,

    Moura, A. P. S., Grebogi, C.
    Physical Review Letters, vol. 86, pp. 2778-2781
    Contributions to Journals: Articles

  • Reconstruction of Information-bearing Chaotic Signals in Additive White Gaussian Noise: Performance Analysis and Evaluation

    Grebogi, C., Marino, J. P., Rosa, E.
    International Journal of Bifurcation and Chaos, vol. 11, pp. 2631-2636
    Contributions to Journals: Articles

  • Riddled Basins and Unstable Dimension Variability in Chaotic Systems With and Without Symmetry

    Grebogi, C., Viana, R. L.
    International Journal of Bifurcation and Chaos, vol. 11, pp. 2689-2698
    Contributions to Journals: Articles

  • Signal Dropout Reconstruction in Communicating with Chaos

    Grebogi, C., Valladares, D. L., Boccaletti, C., Mancini, H.
    International Journal of Bifurcation and Chaos, vol. 11, pp. 2621-2625
    Contributions to Journals: Articles

  • Feedback synchronization using pole-placement control

    Tonelli, R., Lai, Y. C., Grebogi, C., Lai, Y.
    International Journal of Bifurcation and Chaos, vol. 10, no. 11, pp. 2611-2617
    Contributions to Journals: Articles

  • Topology of high-dimensional chaotic scattering

    Lai, Y. C., de Moura, A. P. S., Grebogi, C., Lai, Y.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 62, no. 5, pp. 6421-6428
    Contributions to Journals: Articles

  • Integrated chaotic communication scheme

    Baptista, M. S., Macau, E. E., Grebogi, C., Lai, Y. C., Rosa, E.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 62, no. 4, pp. 4835-4845
    Contributions to Journals: Articles

  • Exploiting the natural redundancy of chaotic signals in communication systems

    Marino, I. P., Rosa, E., Grebogi, C.
    Physical Review Letters, vol. 85, no. 12, pp. 2629-2632
    Contributions to Journals: Articles

  • Comment on "Riddling of chaotic sets in periodic windows" - Lai and Grebogi reply

    Lai, Y. C., Grebogi, C., Lai, Y.
    Physical Review Letters, vol. 85, no. 2, pp. 473-473
    Contributions to Journals: Articles

  • Unstable dimension variability and synchronization of chaotic systems

    Viana, R. L., Grebogi, C.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 62, no. 1, pp. 462-468
    Contributions to Journals: Articles

  • Analog to digital conversion in physical measurements

    Kapitaniak, T., Zyczkowski, K., Feudel, U., Grebogi, C.
    Chaos, Solitons & Fractals, vol. 11, no. 8, pp. 1247-1251
    Contributions to Journals: Articles

  • Bifurcations in two-dimensional piecewise smooth maps: Theory and applications in switching circuits

    Banerjee, S., Ranjan, P., Grebogi, C.
    IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications, vol. 47, no. 5, pp. 633-643
    Contributions to Journals: Articles

  • The control of chaos: theory and applications

    Boccaletti, S., Grebogi, C., Lai, Y. C., Mancini, H., Maza, D., Lai, Y.
    Physics Reports, vol. 329, no. 3, pp. 103-197
    Contributions to Journals: Articles

  • Topological scaling and gap filling at crisis

    Szabo, K. G., Lai, Y. C., Tel, T., Grebogi, C., Lai, Y.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 61, no. 5, pp. 5019-5032
    Contributions to Journals: Articles

  • Communication through chaotic modeling of languages

    Baptista, M. S., Rosa, E., Grebogi, C.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 61, no. 4, pp. 3590-3600
    Contributions to Journals: Articles

  • Chaotic advection, diffusion, and reactions in open flows

    Tel, T., Karolyi, G., Pentek, A., Scheuring, I., Toroczkai, Z., Grebogi, C., Kadtke, J.
    Chaos, vol. 10, no. 1, pp. 89-98
    Contributions to Journals: Articles

  • Obstruction to deterministic modeling of chaotic systems with an invariant subspace

    Lai, Y. C., Grebogi, C., Lai, Y.
    International Journal of Bifurcation and Chaos, vol. 10, no. 3, pp. 683-693
    Contributions to Journals: Articles
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