The chaotic behaviour of piecewise smooth differential equations on two-dimensional torus and sphere

Autor(es)

Martins, Ricardo M. ^[1] ; Tonon, Durval J. ^[2]

Afiliação do(s) autor(es)

^[1] Campinas Univ, Inst Math Stat & Sci Comp, Campinas, SP - Brazil

^[2] Univ Fed Goias, Inst Math & Stat, Goiania, Go - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 34, n. 2, p. 356-373, APR 3 2019.
• Citações Web of Science: 0

Resumo

This paper studies the global dynamics of piecewise smooth differential equations defined in the two-dimensional torus and sphere in the case when the switching manifold breaks the manifold into two connected components. Over the switching manifold, we consider the Filippov's convention for discontinuous differential equations. The study of piecewise smooth dynamical systems over torus and sphere is common for maps and up to where we know this is the first characterization for piecewise smooth flows arising from solutions of differential equations. We provide conditions under generic families of piecewise smooth equations to get periodic and dense trajectories. Considering these generic families of piecewise differential equations, we prove that a non-deterministic chaotic behaviour appears. Global bifurcations are also classified. (AU)

• Processo FAPESP: 15/06903-8 - Conjuntos minimais em sistemas dinâmicos não-suaves
• Beneficiário: Ricardo Miranda Martins
• Modalidade de apoio: Auxílio à Pesquisa - Regular