Author(s): Carvalho, Tiago ; Duarte Novaes, Douglas ; Gonçalves, Luiz Fernando [UNESP]
Date: 2020
Persistent ID: http://hdl.handle.net/11449/198854
Origin: Oasisbr
Subject(s): Chaos; Piecewise smooth vector fields; Prey switching model; Shilnikov connection; Sliding dynamics
Made available in DSpace on 2020-12-12T01:23:47Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-05-01
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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.
Departamento de Computação e Matemática Faculdade de Filosofia Ciências e Letras de Ribeirão Preto Universidade de São Paulo, Av. Bandeirantes, 3900
Departamento de Matemática Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda 651, Cidade Universitária Zeferino Vaz
Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP), Rua Cristóvão Colombo, 2265
Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP), Rua Cristóvão Colombo, 2265
FAPESP: 2017/00883-0
FAPESP: 2018/13481-0
FAPESP: 2018/16430-8
FAPESP: 2019/10269-3
CNPq: 306649/2018-7
CNPq: 438975/2018-9
CAPES: Finance Code 001
