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arXiv · 1809.02060

Sliding Shilnikov Connection in Filippov-type Predator-Prey Model

Tiago de Carvalho·Douglas Duarte Novaes·Luiz Fernando Gonçalves
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Abstract

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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Tiago de Carvalho, Douglas Duarte Novaes, Luiz Fernando Gonçalves. 2018-09-06. Sliding Shilnikov Connection in Filippov-type Predator-Prey Model. https://doi.org/10.1007/s11071-020-05672-w

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