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Updated: Jul 16, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two
1Department of Theoretical Ecology, Institute of Entomology, Biology Center, Academy of Sciences of the Czech Republic, Ceské Budejovice, Czech Republic. krivan@entu.cas.cz
Abstract:
In this article we construct Lyapunov functions for models described by piecewise-continuous and independent differential equations. Because these models are described by discontinuous differential equations, the theory of Lyapunov functions for smooth dynamical systems is not applicable. Instead, we use a geometrical approach to construct a Lyapunov function. Then we apply the general approach to analyze population dynamics describing exploitative competition of two species in a two-patch environment. We prove that for any biologically meaningful parameter combination the model has a globally stable equilibrium and we analyze this equilibrium with respect to parameters.
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