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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-01181-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01180-1
Online ISBN: 978-3-642-01181-8
eBook Packages: Computer ScienceComputer Science (R0)