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Hamiltonian structure of the Lotka-Volterra equations

Authors
Journal
Physics Letters A
0375-9601
Publisher
Elsevier
Publication Date
Volume
145
Issue
1
Identifiers
DOI: 10.1016/0375-9601(90)90270-x

Abstract

Abstract The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

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