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Dynamics of a predator-prey model with non-monotonic response function
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Broer, H. W., Saleh, K., Naudot, V. and Roussarie, R. (2007) Dynamics of a predator-prey model with non-monotonic response function. In: International Conference on Nonautonomous and Stochastic Dynamical Systems, Univ Sevilla, Seville, Spain, September 29-October 02, 2005. Published in: Discrete and Continuous Dynamical Systems, Vol.18 (No.2-3). pp. 221-251. ISSN 1078-0947.
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Abstract
A five-parameter family of planar vector fields, which models the dynamics of certain populations of predators and their prey, is discussed. The family is a variation of the classical Volterra-Lotka system by taking into account group defense strategy, 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, the bifurcations between the various domains of structural stability are investigated. It is possible to fix the values of two of the parameters and study the bifurcations in terms of the remaining three. Here we find several codimension 3 bifurcations that form organizing centres 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.
| Item Type: | Conference Item (UNSPECIFIED) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Discrete and Continuous Dynamical Systems | ||||
| Publisher: | American Institute of Mathematical Sciences | ||||
| ISSN: | 1078-0947 | ||||
| Official Date: | June 2007 | ||||
| Dates: |
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| Volume: | Vol.18 | ||||
| Number: | No.2-3 | ||||
| Number of Pages: | 31 | ||||
| Page Range: | pp. 221-251 | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Title of Event: | International Conference on Nonautonomous and Stochastic Dynamical Systems | ||||
| Type of Event: | Conference | ||||
| Location of Event: | Univ Sevilla, Seville, Spain | ||||
| Date(s) of Event: | September 29-October 02, 2005 |
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