1.
Tiago de Carvalho; Douglas D. Novaes; Luis Fernando Gonçalves
Sliding Shilnikov Connection in Filippov-type Predator-Prey Model Journal Article
Em: Nonlinear Dynamics, vol. 100, pp. 2973-2987, 2020.
@article{deCarNov2020,
title = {Sliding Shilnikov Connection in Filippov-type Predator-Prey Model},
author = {Tiago de Carvalho and Douglas D. Novaes and Luis Fernando Gonçalves},
url = {http://arxiv.org/abs/1809.02060},
doi = {10.1007/s11071-020-05672-w},
year = {2020},
date = {2020-05-13},
journal = {Nonlinear Dynamics},
volume = {100},
pages = {2973-2987},
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.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
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.
