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Chaotic dynamics and coexistence in a three species interaction model. (English) Zbl 1328.92066

Summary: This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of dynamical systems we prove that the trajectories of system are bounded and that open subsets of parameters exist, such that the system in the first octant has at most two singularities. For an open subset of the parameters space, the system is shown to have an invariant compact set and this is a topologically transitive attractor set. Finally, we find another open set in the parameters space, such that the system has two limit cycles each contained in different invariant planes. The work is completed with a numeric simulation showing the attractor is a strange attractor.

MSC:

92D25 Population dynamics (general)
34D35 Stability of manifolds of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Software:

Mathematica
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References:

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