Seminário de Sistemas Dinâmicos 2023/1

Seminário 10: 27/06/2023

Palestrante: Letícia Cândido - IMECC/Unicamp

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

Resumo: 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

1 AFRAIMOVICH, V. S.; NIKOV, L. P. S. Strange attractors and quasiattractors. In: Nonlinear dynamics and turbulence. [S.l.]: Pitman, Boston, MA, 1983, (Interaction Mech. Math. Ser.). p. 1–34. ISBN 0-273-08560-3. páginas

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

3 NOVAES, D. D.; TEIXEIRA, M. A. Shilnikov problem in Filippov dynamical systems. Chaos, v. 29, n. 6, p. 063110, 8, 2019. ISSN 1054-1500,1089-7682. Disponível em: . páginas

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

5 GUARDIA, M.; SEARA, T. M.; TEIXEIRA, M. A. Generic bifurcations of low codimension of planar Filippov systems. J. Differential Equations, v. 250, n. 4, p. 1967– 2023, 2011. ISSN 0022-0396,1090-2732. Disponível em: . páginas

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

Horário: 10h

O seminário ocorrerá de maneira remota.

Sala virtual: meet.google.com/fvg-pmit-xud