Abstract
Effects of parameter mismatches in synchronized time series are studied first for an analytical non-linear dynamical system (coupled logistic map, CLM) and then in a real system (Electroencephalograph (EEG) signals). The internal system parameters derived from GP analysis are shown to be quite effective in understanding aspects of synchronization and non-synchronization in the two systems considered. In particular, GP is also successful in generating the CLM coupled equations to a very good accuracy with reasonable multi-step predictions. It is shown that synchronization in the above two systems is well understood in terms of parameter mismatches in the system equations derived by GP approach.
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References
Ding, M.L., Ding, E.L., Ditto, W.L., Gluckman, B., In, V., Peng, J.H., Spano, M.L., Yang, W.M.: Control and Synchronization of Chaos in High Dimensional Systems: Review of Some Recent Results. Chaos 7, 644–652 (1997)
Strogatz, S.H.: From Kuramoto to Crawford: Exploring the Onset of Synchroniztion in Populations of Coupled Oscillators. Physica D 143, 1–20 (2000)
Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)
Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The Synchronization of Chaotic Systems. Physics Reports - Review Section of Physics Letters 366, 1–101 (2002)
Andrzejak, R.G., Lehnertz, K., Mormann, F., Rieke, C., David, P., Elger, C.E.: Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state. Physical Review EÂ 64, 061907 (2001)
Fogel, D.B.: Evolutionary Computation, The Fossil Record. IEEE Press, Los Alamitos (1998)
Holland, J.H.: Adaptation in Natural and Artificial Systems, 2nd edn. University of Michigan Press, Ann Arbor (1975)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley Publication, Reading (1989)
Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press, Cambridge (1996)
Szpiro, G.G.: Forecasting Chaotic Time Series With Genetic Algorithms. Physical Review EÂ 55, 2557 (1997)
Abarbanel, H., Brown, R., Sidorovich, J., Tsimring, L.: The Analysis of Observed Chaotic Data in Physical Systems. Rev. of Mod. Phys. 65, 1331 (1993)
Ahalpara, D.P., Parikh, J.C.: Genetic Programming Based Approach for Modeling Time Series Data of Real Systems. International Journal of Modern Physics C 19(1), 63–91 (2008)
Ahalpara, D.P., Panigrahi, P.K., Parikh, J.C.: Variations in Financial Time Series: Modelling Through Wavelets and Genetic Programming. In: Chatterjee, A., Chakrabarti, B.K. (eds.) Econophysics of Markets and Business Networks. Proceedings of the Econophys-Kolkata III, vol. 35. Springer, Heidelberg (2007)
Santhanam, M.S., Patra, P.K.: Statistics of Atmospheric Correlations. Phys. Rev. E64, 016102 (2001)
Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia (1992)
Manimaran, P., Panigrahi, P.K., Parikh, J.C.: Multiresolution Analysis of Stock Market Price Fluctuations. Phys. Rev. E72, 046120 (2005)
Ahalpara, D.P., Parikh, J.C.: Modeling Time Series Data of Real Systems. International Journal of Modern Physics C 18(2), 235–252 (2007)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: The Art of Scientific Computing, 2nd edn., p. 200. Cambridge University Press, Cambridge (1993)
Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (1997)
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Ahalpara, D.P., Arora, S., Santhanam, M.S. (2009). Genetic Programming Based Approach for Synchronization with Parameter Mismatches in EEG. In: Vanneschi, L., Gustafson, S., Moraglio, A., De Falco, I., Ebner, M. (eds) Genetic Programming. EuroGP 2009. Lecture Notes in Computer Science, vol 5481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01181-8_2
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DOI: https://doi.org/10.1007/978-3-642-01181-8_2
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