“Limit cycles and Hopf bifurcations in a Kolmogorov type system”

Authors: Simona Muratori and Sergio Rinaldi,
Affiliation: Politecnico di Milano (Italy)
Reference: 1989, Vol 10, No 2, pp. 91-99.

Keywords: Non-linear systems, limit cycle, Hopf bifurcation, Poincare index, stability, prey-predator models

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 intra-specific 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 be specified analytically.

PDF PDF (537 Kb)        DOI: 10.4173/mic.1989.2.3

DOI forward links to this article:
[1] Simona Muratori and Sergio Rinaldi (1989), doi:10.1016/0307-904X(89)90160-1
[2] S. Rinaldi and S. Muratori (1992), doi:10.1016/0040-5809(92)90048-X
[3] Simona Muratori (1991), doi:10.1016/0096-3003(91)90091-Z
[4] Florian Rupp and Jürgen Scheurle (2015), doi:10.1002/mma.3347
[5] Djamila Djedid, Jaume Llibre and Amar Makhlouf (2020), doi:10.1016/j.chaos.2020.110489
[6] Giuseppe Orlando and Mario Sportelli (2021), doi:10.1007/978-3-030-70982-2_14
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  title={{Limit cycles and Hopf bifurcations in a Kolmogorov type system}},
  author={Muratori, Simona and Rinaldi, Sergio},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}