A computational framework for finding parameter sets associated with chaotic dynamics

Author:

Koshy-Chenthittayil S.1,Dimitrova E.2,Jenkins E.W.3,Dean B.C.4

Affiliation:

1. Center for Quantitative Medicine, UConn Health, Farmington, USA

2. Department of Mathematics, California Polytechnic State University, San Luis Obispo, USA

3. School of Mathematical and Statistical Sciences, Clemson University, Clemson, USA

4. School of Computing, Clemson University, Clemson, USA

Abstract

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software’s optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.

Publisher

IOS Press

Subject

Computational Theory and Mathematics,Computational Mathematics,Genetics,Molecular Biology,General Medicine

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