GSD Seminar 2023/1

Seminar 10

June 27, 2023

Speaker: Letícia Cândido - IMECC/Unicamp

Title: Sliding Shilnikov Orbit: theoretical aspects and applications in biological systems

Abstract:

This work is inspired by the work of Shilnikov in (1, 2). An interesting behavior can be observed in smooth vector fields, where a trajectory connects an equilibrium point to itself, which we call homoclinic orbit. Shilnikov studied a special kind of homoclinic orbit and the behavior of the vector field close to it. Since the study of piecewise smooth vector fields is of our interest, we are going to generalize the definition of homoclinic orbit for the piecewise context. Using this, we can study the behavior close to this orbit and prove a chaotic of the trajectories.

Keywords: Sliding Shilnikov Orbit, Piecewise Vector Field, Bernoulli Shift, Chaos.

References

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2 NIKOV, L. P. Šil. Existence of a countable set of periodic motions in a neighborhood of a homoclinic curve. Dokl. Akad. Nauk SSSR, p. 298–301, 1967. ISSN 0002-3264. páginas

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4 NOVAES, D. D.; PONCE, G.; aO, R. V. Chaos induced by sliding phenomena in Filippov systems. J. Dynam. Differential Equations, v. 29, n. 4, p. 1569– 1583, 2017. ISSN 1040-7294,1572-9222. Disponível em: . páginas

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6 DUMORTIER, F.; LLIBRE, J.; ARTéS, J. C. Qualitative theory of planar differential systems. [S.l.]: Springer-Verlag, 2 Berlin, 2006. xvi+298 p. (Universitext). ISBN 3-540-32893-9. páginas

7 SOTOMAYOR, J. Generic bifurcations of dynamical systems. In: Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971),. [S.l.]: „ 1973. p. 561–582. páginas

8 SOTOMAYOR, J. Lições de equações diferenciais ordinárias. [S.l.]: Instituto de Matemática Pura e Aplicada, Rio de Janeiro„, 1979. xvi+327 p. páginas

Time: 10:00 GMT-3

Virtual Room: meet.google.com/fvg-pmit-xud