Sliding Shilnikov connection in Filippov-type predator–prey model
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2020-05-01
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Resumo
Recently, a piecewise smooth differential system was derived as a model of a 1 predator–2 prey interaction where the predator feeds adaptively on its preferred prey and an alternative prey. In such a model, strong evidence of chaotic behavior was numerically found. Here, we revisit this model and prove the existence of a Shilnikov sliding connection when the parameters are taken in a codimension one submanifold of the parameter space. As a consequence of this connection, we conclude, analytically, that the model behaves chaotically for an open region of the parameter space.
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Chaos, Piecewise smooth vector fields, Prey switching model, Shilnikov connection, Sliding dynamics
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Nonlinear Dynamics, v. 100, n. 3, p. 2973-2987, 2020.