Chaotic behaviour of a predator-prey system
Generally a predator-prey system is modelled by two ordinary differential equations which describe the rate of changes of the biomasses. Since such a system is two-dimensional no chaotic behaviour can occur. In the popular Rosenzweig-MacArthur model, which replaced the Lotka-Volterra model, a stable equilibrium or a stable limit cycle exist. In this paper the prey consumes a non-viable nutrient whose. dynamics is modelled explicitly and this gives an extra ordinary differential equation. For a predator-prey system under chemostat conditions where all parameter values are biologically meaningful, coexistence of multiple chaotic attractors is possible in a narrow region of the two-parameter bifurcation diagram with respect to the chemostat control parameters. Crisis-limited chaotic behaviour and a bifurcation point where two coexisting chaotic attractors merge will be discussed. The interior and boundary crises of this continuous-time predator-prey system look similar to those found for the discrete-time Henon map. The link is via a Poincare map for a suitable chosen Poincare plane where the predator attains an extremum. Global homoclinic bifurcations, are associated with boundary and interior crises
| Main Authors: | , |
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| Format: | Article/Letter to editor biblioteca |
| Language: | English |
| Subjects: | attractors, crises, |
| Online Access: | https://research.wur.nl/en/publications/chaotic-behaviour-of-a-predator-prey-system |
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