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arXiv · 1910.03309

Local Stability and Lyapunov Functionals for n-Dimensional Quasipolynomial Conservative Systems

Benito Hernández-Bermejo·Victor Fairén
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Abstract

We present a method for determining the local stability of equilibrium points of conservative generalizations of the Lotka-Volterra equations. These generalizations incorporate both an arbitrary number of species -including odd-dimensional systems- and nonlinearities of arbitrarily high order in the interspecific interaction terms. The method combines a reformulation of the equations in terms of a Poisson structure and the construction of their Lyapunov functionals via the energy-Casimir method. These Lyapunov functionals are a generalization of those traditionally known for Lotka-Volterra systems. Examples are given.

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BibTeXRIS

Benito Hernández-Bermejo, Victor Fairén. 2019-10-08. Local Stability and Lyapunov Functionals for n-Dimensional Quasipolynomial Conservative Systems. https://doi.org/10.1006/jmaa.2000.7318

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