Limit cycles and Hopf bifurcations in a Kolmogorov type system
Open Access
- 1 January 1989
- journal article
- research article
- Published by Norwegian Society of Automatic Control in Modeling, Identification and Control: A Norwegian Research Bulletin
- Vol. 10 (2) , 91-99
- https://doi.org/10.4173/mic.1989.2.3
Abstract
The paper is devoted to the study of a class of Kolmogorov type systems which can be used to represent the dynamic behaviour of prey and predators. The model is an extension of the classical prey-predator model since it allows intraspecific competition for the predator''s species. The analysis shows that the system can only have Kolmogorov''s two modes of behaviour: a globally stable equilibrium or a globally stable limit cycle. Moreover, the transition from one of these two modes to the other is a non-catastrophic Hopf bifurcation which can easily be specified analytically.This publication has 6 references indexed in Scilit:
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