A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two patch environments.
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.
Krivan
Vlastimil
V
Department of Theoretical Ecology, Institute of Entomology, Biology Center, Academy of Sciences of the Czech Republic, Ceské Budejovice, Czech Republic. krivan@entu.cas.cz
Vrkoc
Ivo
I
D000818:Animals; D017753:Ecosystem; D016014:Linear Models; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics