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.
@article{arxiv.1809.02060,
title = {Sliding Shilnikov Connection in Filippov-type Predator-Prey Model},
author = {Tiago de Carvalho and Douglas Duarte Novaes and Luiz Fernando Gonçalves},
journal= {arXiv preprint arXiv:1809.02060},
year = {2020}
}