2.
Tiago de Carvalho; Douglas D. Novaes; Durval J. Tonon
Sliding motion on tangential sets of Filippov systems Journal Article
Em: Preprint, 2021.
@article{CarNovTon2021,
title = {Sliding motion on tangential sets of Filippov systems},
author = {Tiago de Carvalho and Douglas D. Novaes and Durval J. Tonon},
url = {https://arxiv.org/abs/2111.12377},
year = {2021},
date = {2021-11-25},
journal = {Preprint},
abstract = {We consider piecewise smooth vector fields $Z=(Z_+, Z_-)$ defined in $R^n$ where both vector fields are tangent to the switching manifold $Sigma$ along a manifold $M$. Our main purpose is to study the existence of an invariant vector field defined on $M$, that we call {it tangential sliding vector field}. We provide necessary and sufficient conditions under $Z$ to characterize the existence of this vector field. Considering a regularization process, we proved that this tangential sliding vector field is topological equivalent to an invariant dynamics under the slow manifold. Besides then, at the end of the work we apply the results in a system that governs the intermittent treatment of HIV.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We consider piecewise smooth vector fields $Z=(Z_+, Z_-)$ defined in $R^n$ where both vector fields are tangent to the switching manifold $Sigma$ along a manifold $M$. Our main purpose is to study the existence of an invariant vector field defined on $M$, that we call {it tangential sliding vector field}. We provide necessary and sufficient conditions under $Z$ to characterize the existence of this vector field. Considering a regularization process, we proved that this tangential sliding vector field is topological equivalent to an invariant dynamics under the slow manifold. Besides then, at the end of the work we apply the results in a system that governs the intermittent treatment of HIV.
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.
