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This article is cited in 18 scientific papers (total in 18 papers)
On the 70th birthday of L.P. Shilnikov
A predator-prey model with non-monotonic response function
H. W. Broera, R. Roussarieb, V. Naudota, K. Saleha a Department of Mathematics, University of Groningen,
P.O. Box 800, 9700 AV Groningen, The Netherlands
b Institut Mathématiques de Bourgogne, CNRS,
9, avenue Alain Savary, B.P. 47 870, 21078 Dijon cedex, France
Abstract:
We study the dynamics of a family of planar vector fields that models certain populations of predators and their prey. This model is adapted from the standard Volterra–Lotka system by taking into account group defense, competition between prey and competition between predators. Also we initiate computer-assisted research on time-periodic perturbations, which model seasonal dependence.
We are interested in persistent features. For the planar autonomous model this amounts to structurally stable phase portraits. We focus on the attractors, where it turns out that multi-stability occurs. Further, we study the bifurcations between the various domains of structural stability. It is possible to fix the values of two of the parameters and study the bifurcations in terms of the remaining three. We find several codimension 3 bifurcations that form organizing centers for the global bifurcation set.
Studying the time-periodic system, our main interest is the chaotic dynamics. We plot several numerical examples of strange attractors.
Keywords:
predator-prey dynamics, organizing center, bi-furcation, strange attractor.
Received: 01.08.2005 Accepted: 01.09.2005
Citation:
H. W. Broer, R. Roussarie, V. Naudot, K. Saleh, “A predator-prey model with non-monotonic response function”, Regul. Chaotic Dyn., 11:2 (2006), 155–165
Linking options:
https://www.mathnet.ru/eng/rcd665 https://www.mathnet.ru/eng/rcd/v11/i2/p155
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