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A computational framework for finding parameter sets associated with chaotic dynamics.

S Koshy-Chenthittayil¹, E Dimitrova², E W Jenkins³

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

In Silico Biology

|April 26, 2021

Summary

This summary is machine-generated.

Researchers used software tools to find chaotic behavior in biological systems by identifying positive Lyapunov exponents. They found that small search spaces can miss chaotic dynamics, highlighting the importance of thorough parameter exploration.

Keywords:

Chaotic dynamics Lyapunov exponent genetic algorithm parallel coordinate plot population dynamics

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Area of Science:

Ecology
Dynamical Systems Theory
Computational Biology

Background:

Biological ecosystems can display complex, chaotic dynamics.
Dynamical systems models are used to analyze these behaviors analytically and empirically.
Identifying chaotic regions requires finding positive Lyapunov exponents.

Purpose of the Study:

To evaluate the capability of existing software tools (COPASI, R) in identifying chaotic behavior in biological dynamical systems.
To explore the effectiveness of optimization algorithms in finding positive Lyapunov exponents within parameter spaces.
To investigate the impact of parameter space granularity on the detection of chaos.

Main Methods:

Utilized COPASI and R software for dynamical systems analysis.
Employed optimization algorithms to search for parameter sets yielding positive Lyapunov exponents.
Examined multiple dynamical systems models representing biological populations.
Varied the spacing of independent variables in the parameter space search.

Main Results:

Software optimization algorithms successfully identified parameter sets leading to positive Lyapunov exponents.
Chaotic regions, even those with small support, were discoverable.
For one system, a search with small parameter spacing failed to uncover positive Lyapunov exponents.

Conclusions:

Existing software tools are effective in detecting chaos in biological models.
Thorough exploration of parameter space is crucial for uncovering chaotic dynamics.
The granularity of the search significantly impacts the ability to find chaotic regimes.