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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Sliding Shilnikov connection in Filippov-type predator-prey model

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Author(s):
Carvalho, Tiago [1] ; Novaes, Douglas Duarte [2] ; Goncalves, Luiz Fernando [3]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Fac Filosofia Ciencias & Letras Ribeirao Preto, Dept Comp & Matemat, Av Bandeirantes 3900, BR-14040901 Ribeirao Preto, SP - Brazil
[2] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
[3] Univ Estadual Paulista, UNESP, Inst Biociencias Letras & Ciencias Exatas, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: NONLINEAR DYNAMICS; v. 100, n. 3 MAY 2020.
Web of Science Citations: 0
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. (AU)

FAPESP's process: 17/00883-0 - Piecewise smooth vector fields with applications in biology
Grantee:Tiago de Carvalho
Support Opportunities: Regular Research Grants
FAPESP's process: 19/10450-0 - Piecewise smooth vector fields: Closing Lemmas, shifts and horseshoe dynamics.
Grantee:Tiago de Carvalho
Support Opportunities: Regular Research Grants
FAPESP's process: 18/16430-8 - Global dynamics of nonsmooth differential equations
Grantee:Douglas Duarte Novaes
Support Opportunities: Regular Research Grants
FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants