Center for Quantitative Medicine, UConn Health, Farmington, USA.
Department of Mathematics, California Polytechnic State University, San Luis Obispo, USA.
In Silico Biol. 2021;14(1-2):41-51. doi: 10.3233/ISB-200476.
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.
许多生物生态系统表现出混沌行为，可以通过在相关动力系统模型中选择参数进行分析，或者通过对实验数据进行分析来进行实证研究。在本文中，我们使用现有的软件工具（COPASI、R）来探索动力系统，并发现存在正 Lyapunov 指数的区域，从而存在混沌。我们评估了软件的优化算法在使用几种生物种群模型的动力系统中寻找这些正数值的能力。这些算法已经能够识别导致正 Lyapunov 指数的参数集，即使这些指数存在于支持较小的区域。对于所检查的系统之一，我们观察到，当在参数空间中以独立变量值之间的小间距执行搜索时，并没有发现正 Lyapunov 指数。
