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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.)

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

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Martins, Ricardo M. [1] ; Tonon, Durval J. [2]
Total Authors: 2
[1] Campinas Univ, Inst Math Stat & Sci Comp, Campinas, SP - Brazil
[2] Univ Fed Goias, Inst Math & Stat, Goiania, Go - Brazil
Total Affiliations: 2
Document type: Journal article
Source: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 34, n. 2, p. 356-373, APR 3 2019.
Web of Science Citations: 0

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)

FAPESP's process: 15/06903-8 - Minimal sets in non-smooth dynamical systems
Grantee:Ricardo Miranda Martins
Support Opportunities: Regular Research Grants