Taiwanese Journal of Mathematics

A SURVEY OF CONSTRUCTING LYAPUNOV FUNCTIONS FOR MATHEMATICAL MODELS IN POPULATION BIOLOGY

Sze-Bi Hsu

Abstract

In this paper we survey the construction of Lyapunov functions (or functionals) for various ecological models which take the form of ODE systems (or Reaction-Diffusion PDE systems). First we consider the resources-consumers type ecological models which study the competition of $n$ microorgansims for a single limiting resource or two complementary resources in the chemostat. Next we consider the Gause-type predator-prey systems and the Lesile-type predator-prey systems. From the Lyapunov functions of the predator-prey system we construct new Lyapunov functions for three-level food chain models and one prey two predators models. Suppose a Lyapunov function is known for an ecological model which takes the form of an ODE system. Then we construct a Lyapunov functional for the corresponding reaction-diffusion PDE systems. Open problems are indicated when there is gap in the theory.

Article information

Source
Taiwanese J. Math., Volume 9, Number 2 (2005), 151-173.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407791

Digital Object Identifier
doi:10.11650/twjm/1500407791

Mathematical Reviews number (MathSciNet)
MR2142410

Zentralblatt MATH identifier
1087.34031

Citation

Hsu, Sze-Bi. A SURVEY OF CONSTRUCTING LYAPUNOV FUNCTIONS FOR MATHEMATICAL MODELS IN POPULATION BIOLOGY. Taiwanese J. Math. 9 (2005), no. 2, 151--173. doi:10.11650/twjm/1500407791. https://projecteuclid.org/euclid.twjm/1500407791

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