Dr MURILO DA SILVA BAPTISTA

Dr MURILO DA SILVA BAPTISTA The University of Aberdeen School of Natural & Computing Sciences Senior Lecturer work +44 (0)1224 272489

Senior Lecturer

Personal Details

Telephone: +44 (0)1224 272489
Email: murilo.baptista@abdn.ac.uk
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Research interests

1. Synchronization and information in dynamical networks:

I believe that the understanding of how and how much information a chaotic network is able to transmit, the network capacity, is the key to understanding how and how much information is transmitted in a large class of dynamical networks, in particular our brain. We have shown that similar to a typical communication channel, also a chaotic neural network possess its own information capacity which limits the amount of information that can be transmitted through it. This capacity, which we are able to analytically or semi-analytically calculate,  is a function of the network topology, the dynamics of the nodes describing the network and the level of synchronization among the nodes of the network. 

I am also interested in understanding the onset of synchronization in networks whose nodes are connected with both linear (electrical connection in neural networks) and non-linear ways (chemical connection in neural networks), and when the nodes of the network have non-equal dynamic descriptions. 


2. Fundamentals of dynamical systems:

I have been working to show how to extract relevant invariant quantities in dynamical systems (e.g. Kolmogorov-Sinai entropy) by using recurrence times, in particular Poincaré recurrences, that measure the time interval for a  system to return to a configuration close to its initial state. Our most recent result shows how to calculate the probability density of Poincaré returns through the use of only a few unstable periodic orbits.

3. Data driving modellings:

I have three approaches to model a complex system from data sets: measuring how much time it takes for a system to return to some approximate state (recurrence times), by analysing a symbolic representation of the data, and by identifying functional (mutual information) relationships between two nodes or two data sets.

  • Recurrence times: the main argument of using recurrence times to model complex systems is that one can easily have experimental access to them.  The belief and the hope is that from them one can construct reasonable models from the system being observed. 
  • Symbolic models: representing a data set measured at a time by x(t), with x belonging to the real set, it is often unknown how to predict x(t+delta). Encoding x(t) by a set of N finite symbols S={s_1,s_2,...,s_N} might allow one to predict S(t+delta) based on the information about S(t). These models give an approximate description of the future.
  • Functional models: I am also interested in identifying nodes in a complex network that exchange higher levels of information or two data sets from a complex system that share high amounts of information. Knowing whether two nodes or two data sets share high amounts of information is a way to understanding whether they are functionally connected. This information

4. Phase and phase synchronization:

The phase is a fundamental dynamical quantity for studying synchronization and the transmission of information in complex networks. This quantity is closely related to the way neurons (and other cells) transmit information to each other.  Even though we can already calculate the phase of many possible oscillators, which allow us to measure the phenomenon of phase synchronization, there is still a large class of (non-coherent) oscillators such as neurons, where the phase cannot be well defined, in terms of the vector field, and one has to employ alternative data analysis approaches as the Hilbert transformation. I aim to find a general description of phase for a large class of vector fields.

5. Technological applications:

Communication: chaos-based communication is a promising alternative to create secure and reliable communication systems. Due to its nature, chaos naturally provides many of the protocols currently being used in the modern digital communication systems. I am currently working on a chaos-based method to transmit information in underwater environments.

Energy: consumers and generators must operate in synchrony for a power-grid to function efficiently. I am currrently working to understand which are the clonditions (capacity of transmission lines, connecting topology of the grid) that makes a power-grid to work efficiently.   


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Publications

Contributions to Journals

Articles

  • Baptista, MDS. (in press). 'Active networks that maximize information transmission'. International Journal of Bifurcation and Chaos.
  • Baptista, MDS. (2011). 'Density of first Poincaré returns, periodic orbits, and Kolmogorov–Sinai entropy'. Communications in Nonlinear Science & Numerical Simulation, vol 16, no. 2, pp. 863 -875.
    [Online] DOI: 10.1016/j.cnsns.2010.05.018
  • Baptista, MS., Kakmeni, FM., Del Magno, G. & Hussein, MS. (2011). 'How complex a dynamical network can be?'. Physics Letters A, vol 375, no. 10, pp. 1309-1318.
    [Online] DOI: 10.1016/j.physleta.2011.01.054
  • Pinto, PRF., Baptista, MS. & Labouriau, IS. (2011). 'Density of first Poincare returns, periodic orbits, and Kolmogorov-Sinai entropy'. Communications in Nonlinear Science & Numerical Simulation, vol 16, no. 2, pp. 863-875.
    [Online] DOI: 10.1016/j.cnsns.2010.05.018
  • Slipantschuk, J., Ullner, E., Baptista, MDS., Zeineddine, M. & Thiel, M. (2010). 'Abundance of stable periodic behavior in a Red Grouse population model with delay: A consequence of homoclinicity'. Chaos, vol 20, no. 4, pp. 045117.
    [Online] DOI: 10.1063/1.3527032
  • 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
  • Baptista, MS., Ngamga, EJ., Pinto, PRF., Brito, M. & Kurths, J. (2010). 'Kolmogorov-Sinai entropy from recurrence times'. Physics Letters A, vol 374, no. 9, pp. 1135-1140.
    [Online] DOI: 10.1016/j.physleta.2009.12.057
  • Baptista, MDS., Maranhão, DM. & Sartorelli, JC. (2009). 'Dynamical estimates of chaotic systems from Poincaré recurrences'. Chaos, vol 19, no. 043115, pp. -.
    [Online] DOI: doi:10.1063/1.3263943
  • Baptista, MDS. & Conti, LA. (2009). 'The Staircase Structure of the Southern Brazilian Continental Shelf'. Mathematical Problems in Engineering, vol 2009, pp. 1-17.
    [Online] DOI: 10.1155/2009/624861
  • Pereira, T., Baptista, MDS., Reyes, MB., Caldas, IL., Sartorelli, JC. & Kurths, J. (2009). 'A Scenario for torus T2 destruction via a global bifurcation'. Chaos, Solitons & Fractals, vol 39, no. 5, pp. 2198-2210.
    [Online] DOI: doi:10.1016/j.chaos.2007.06.115
  • Maranhão, D., Sartorelli, J. & Baptista, MDS. (2009). 'Experimental identification of chaotic fibers'. Chaos, Solitons & Fractals, vol 39, no. 1, pp. 9-16.
    [Online] DOI: 10.1016/j.chaos.2007.01.131
  • Baptista, MDS., Maranhao, DM. & Sartorelli, JC. (2009). 'Dynamical estimates of chaotic systems from Poincare recurrences'. Chaos, vol 19, no. 4, pp. 1-10.
    [Online] DOI: 10.1063/1.3263943
  • Pereira, T., Baptista, MDS., Reyes, MB., Caldas, IL., Sartorelli, JC. & Kurths, J. (2009). 'A scenario for torus T-2 destruction via a global bifurcation'. Chaos, Solitons & Fractals, vol 39, no. 5, pp. 2198-2210.
    [Online] DOI: 10.1016/j.chaos.2007.06.115
  • Baptista, MDS., de Carvalho, JX. & Hussein, MS. (2008). 'Finding quasi-optimal network topologies for information transmission in active networks'. PLoS one, vol 3, no. 10, pp. e3479.
    [Online] DOI: 10.1371/journal.pone.0003479
  • Baptista, MDS., Garcia, S., Dana, SK. & Kurths, J. (2008). 'Transmission of information and synchronization in a pair of coupled chaotic circuits: An experimental overview'. The European Physical Journal. Special Topics, vol 165, no. 1, pp. 119-128.
    [Online] DOI: 10.1140/epjst/e2008-00855-y
  • Pereira, T., Thiel, M., Baptista, MDS. & Kurths, J. (2008). 'Network mutual information and synchronization under time transformations'. New Journal of Physics, vol 10, pp. -.
    [Online] DOI: 10.1088/1367-2630/10/8/083003
  • Kakmeni, FMM. & Baptista, MDS. (2008). 'Synchronization and information transmission in spatio-temporal networks of deformable units'. Prama¯¿a, vol 70, no. 6, pp. 1063-1076.
    [Online] DOI: 10.1007/s12043-008-0111-3
  • Pereira, T., Baptista, MS. & Kurths, J. (2008). 'Phase and average period of chaotic oscillators(vol 362, pg 159, 2007)'. Physics Letters A, vol 372, no. 13, pp. 2339-2340.
    [Online] DOI: 10.1016/j.physleta.2007.09.077
  • Maranhao, DM., Baptista, MDS., Sartorelli, JC. & Caldas, IL. (2008). 'Experimental observation of a complex periodic window'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 77, no. 3, pp. -.
    [Online] DOI: 10.1103/PhysRevE.77.037202
  • Baptista, MS., Bohn, C., Kliegl, R., Engbert, R. & Kurths, J. (2008). 'Reconstruction of eye movements during blinks'. Chaos, vol 18, no. 1, pp. -.
    [Online] DOI: 10.1063/1.2890843
  • Baptista, MS. & Kurths, J. (2008). 'Transmission of information in active networks'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 77, no. 2, pp. -.
    [Online] DOI: 10.1103/PhysRevE.77.026205
  • Pereira, T., Baptista, MS., Kurths, J. & Reyes, MB. (2007). 'Onset of phase synchronization in neurons with chemical synapse'. International Journal of Bifurcation and Chaos, vol 17, no. 10, pp. 3545-3549.
  • Pereira, T., Baptista, MS. & Kurths, J. (2007). 'Detecting phase synchronization by localized maps: Application to neural networks'. Europhysics Letters, vol 77, no. 4.
    [Online] DOI: 10.1209/0295-5075/77/40006
  • Pereira, T., Baptista, MS. & Kurths, J. (2007). 'Phase and average period of chaotic oscillators'. Physics Letters A, vol 362, no. 2-3, pp. 159-165.
    [Online] DOI: 10.1016/j.physleta.2006.09.099
  • Pereira, T., Baptista, MS. & Kurths, J. (2007). 'General framework for phase synchronization through localized sets'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 75, no. 2.
    [Online] DOI: 10.1103/PhysRevE.75.026216
  • 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
  • Medrano-T., RO., Baptista, MS. & Caldas, IL. (2006). 'Shilnikov homoclinic orbit bifurcations in the Chua's circuit'. Chaos, vol 16, no. 4.
    [Online] DOI: 10.1063/1.2401060
  • Baptista, MS., Pereira, T. & Kurths, J. (2006). 'Upper bounds in phase synchronous weak coherent chaotic attractors'. Physica. D, Nonlinear Phenomena, vol 216, no. 2, pp. 260-268.
    [Online] DOI: 10.1016/j.physd.2006.02.007
  • Baptista, MS., Zhou, C. & Kurths, J. (2006). 'Information transmission in phase synchronous chaotic arrays'. Chinese Physics Letters, vol 23, no. 3, pp. 560-563.
    [Online] DOI: 10.1088/0256-307X/23/3/010
  • Pereira, T., Baptista, MS., Reyes, MB., Caldas, IL., Sartorelli, JC. & Kurths, J. (2006). 'Global bifurcation destroying the experimental torus T-2'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 73, no. 1.
    [Online] DOI: 10.1103/PhysRevE.73.017201
  • 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
  • Baptista, MS., Pereira, T., Sartorelli, JC., Caldas, IL. & Kurths, J. (2005). 'Non-transitive maps in phase synchronization'. Physica. D, Nonlinear Phenomena, vol 212, no. 3-4, pp. 216-232.
    [Online] DOI: 10.1016/j.physd.2005.10.003
  • Baptista, MS. & Kurths, J. (2005). 'Chaotic channel'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 72, no. 4.
    [Online] DOI: 10.1103/PhysRevE.72.045202
  • Medrano-T, RO., Baptista, MS. & Caldas, IL. (2005). 'Basic structures of the Shilnikov homoclinic bifurcation scenario'. Chaos, vol 15, no. 3.
    [Online] DOI: 10.1063/1.2031978
  • Baptista, MS., Pereira, T., Sartorelli, JC., Caldas, IL. & Kurths, J. (2004). 'Phase synchronization and invariant measures in sinusoidally perturbed chaotic systems'. Shock Compression of Condensed Matter, vol 742, pp. 325-329.
  • Baptista, MS., Boccaletti, S., Josic, K. & Leyva, I. (2004). 'Irrational phase synchronization'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 69, no. 5.
    [Online] DOI: 10.1103/PhysRevE.69.056228
  • Rodrigues, A., Caldas, IL., Baptista, MS. & Piqueira, JRC. (2004). 'Conditional targeting for communication'. Chaos, Solitons & Fractals, vol 21, no. 5, pp. 1271-1280.
    [Online] DOI: 10.1016/j.chaos.2003.12.048
  • Medrano-T, RO., Baptista, MS. & Caldas, IL. (2003). 'Homoclinic orbits in a piecewise system and their relation with invariant sets'. Physica. D, Nonlinear Phenomena, vol 186, no. 3-4, pp. 133-147.
    [Online] DOI: 10.1016/j.physd.2003.08.002
  • Baptista, MS., Boccaletti, S., Allaria, E., Meucci, R. & Arecchi, FT. (2003). 'Controlling transient dynamics to communicate with homoclinic chaos'. Chaos, vol 13, no. 3, pp. 921-925.
    [Online] DOI: 10.1063/1.1602591
  • Baptista, MS., Silva, TP., Sartorelli, JC., Caldas, IL. & Rosa, E. (2003). 'Phase synchronization in the perturbed Chua circuit'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 67, no. 5, pp. -.
    [Online] DOI: 10.1103/PhysRevE.67.056212
  • Baptista, MS., Caldas, IL., Heller, MVAP. & Ferreira, AA. (2003). 'Periodic driving of plasma turbulence'. Physics of Plasmas, vol 10, no. 5, pp. 1283-1290.
    [Online] DOI: 10.1063/1.1561612
  • Baptista, MS. & Caldas, IL. (2002). 'Stock market dynamics'. Physica. A, Statistical Mechanics and its Applications, vol 312, no. 3-4, pp. 539-564.
    [Online] DOI: 10.1016/S0378-4371(02)00847-6
  • Baptista, MS. & Lopez, L. (2002). 'Information transfer in chaos-based communication'. Physical Review E - Statistical, Nonlinear and Soft Matter Physics, vol 65, no. 5.
    [Online] DOI: 10.1103/PhysRevE.65.055201
  • dos Santos, EP., Baptista, MS. & Caldas, LL. (2002). 'Dealing with final state sensitivity for synchronous communication'. Physica. A, Statistical Mechanics and its Applications, vol 308, no. 1-4, pp. 101-112.
    [Online] DOI: 10.1016/S0378-4371(02)00572-1
  • Baptista, MS., Caldas, IL., de Sa, WP. & Elizondo, JI. (2002). 'Statistics of plasma fluctuations in runaway discharges in TCABR tokamak'. Brazilian Journal of Physics, vol 32, no. 1, pp. 95-99.
    [Online] DOI: 10.1590/S0103-97332002000100018
  • Ferreira, AA., Heller, MVAP., Baptista, MS. & Caldas, IL. (2002). 'Statistics of turbulence induced by magnetic field'. Brazilian Journal of Physics, vol 32, no. 1, pp. 85-88.
    [Online] DOI: 10.1590/S0103-97332002000100016
  • Baptista, MS., Caldas, IL. & Heller, MVAP. (2001). 'Statistics of plasma edge turbulence in tokamaks'. American Institute of Physics Conference Proceedings, vol 563, no. 1, pp. 221-226.
    [Online] DOI: 10.1063/1.1374912
  • Baptista, MS., Caldas, IL., Heller, MVA. & Ferreira, AA. (2001). 'Onset of symmetric plasma turbulence'. Physica. A, Statistical Mechanics and its Applications, vol 301, no. 1-4, pp. 150-162.
    [Online] DOI: 10.1016/S0378-4371(01)00395-8
  • Baptista, MS., Caldas, IL., Heller, MVAP., Ferreira, AA., Bengtson, RD. & Stockel, J. (2001). 'Recurrence in plasma edge turbulence'. Physics of Plasmas, vol 8, no. 10, pp. 4455-4462.
    [Online] DOI: 10.1063/1.1401117
  • Baptista, MS., Caldas, IL., Baptista, MS., Baptista, CS., Ferreira, AA. & Heller, MVAP. (2000). 'Low-dimensional dynamics in observables from complex and higher-dimensional systems'. Physica. A, Statistical Mechanics and its Applications, vol 287, no. 1-2, pp. 91-99.
    [Online] DOI: 10.1016/S0378-4371(00)00448-9
  • 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. & Caldas, IL. (2000). 'On the stock market recurrence'. Physica. A, Statistical Mechanics and its Applications, vol 284, no. 1-4, pp. 348-354.
    [Online] DOI: 10.1016/S0378-4371(00)00226-0
  • 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
  • Baptista, MS. & Caldas, IL. (1999). 'Type-II intermittency in the driven Double Scroll Circuit'. Physica. D, Nonlinear Phenomena, vol 132, no. 3, pp. 325-338.
    [Online] DOI: 10.1016/S0167-2789(99)00037-8
  • Baptista, MS. (1998). 'Targeting applying epsilon-bounded orbit correction perturbations'. International Journal of Bifurcation and Chaos, vol 8, no. 7, pp. 1575-1584.
    [Online] DOI: 10.1142/S0218127498001224
  • Baptista, MS. & Caldas, IL. (1998). 'Phase-locking and bifurcations of the sinusoidally-driven double scroll circuit'. Nonlinear Dynamics, vol 17, no. 2, pp. 119-139.
    [Online] DOI: 10.1023/A:1008284804398
  • Baptista, MS. & Caldas, IL. (1998). 'Dynamics of the two-frequency torus breakdown in the driven double scroll circuit'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 58, no. 4, pp. 4413-4420.
    [Online] DOI: 10.1103/PhysRevE.58.4413
  • Pinto, RD., Goncalves, WM., Sartorelli, JC., Caldas, IL. & Baptista, MS. (1998). 'Interior crises in a dripping faucet experiment'. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol 58, no. 3, pp. 4009-4011.
  • Baptista, MS. & Caldas, IL. (1998). 'Easy-to-implement method to target nonlinear systems'. Chaos, vol 8, no. 1, pp. 290-299.
    [Online] DOI: 10.1063/1.166309
  • Baptista, MS. (1998). 'Cryptography with chaos'. Physics Letters A, vol 240, no. 1-2, pp. 50-54.
    [Online] DOI: 10.1016/S0375-9601(98)00086-3
  • Baptista, MS. & Caldas, IL. (1997). 'The parameter space structure of the kicked logistic map and its stability'. International Journal of Bifurcation and Chaos, vol 7, no. 2, pp. 447-457.
    [Online] DOI: 10.1142/S0218127497000327
  • Baptista, MS. & Caldas, IL. (1996). 'Dynamics of the kicked logistic map'. Chaos, Solitons & Fractals, vol 7, no. 3, pp. 325-336.

Chapters in Books, Reports and Conference Proceedings

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.
  • BAPTISTA, MS. & CALDAS, IL. (1994). 'CONTROL OF TRAJECTORIES OF THE KICKED LOGISTIC MAP'. in HS Wisniewski (ed.), Chaos/Nonlinear Dynamics: Methods and Commercialization vol. 2037, Proceedings of SPIE - the International Society for Optical Engineering, SPIE, pp. 273-284.

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