Stability Analysis of Predator-Prey Models via the Liapunov Method

Gatto, M. and Rinaldi, S. (1975) Stability Analysis of Predator-Prey Models via the Liapunov Method. IIASA Research Memorandum. IIASA, Laxenburg, Austria, RM-75-052

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Abstract

As is well known from the classical applications in the electrical and mechanical sciences, energy is a suitable Liapunov function; thus, by analogy, all energy functions proposed in ecology are potential Liapunov functions. In this paper, a generalized Lotka-Volterra model is considered and the stability properties of its non-trivial equilibrium are studied by means of an energy function first proposed by Volterra in the context of conservative ecosystems. The advantage of this Liapunov function with respect to the one that can be induced through linearization is also illustrated.

Item Type: Monograph (IIASA Research Memorandum)
Research Programs: Resources and Environment Area (REN)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:42
Last Modified: 10 Aug 2016 23:40
URI: http://pure.iiasa.ac.at/464

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