Abstract: In the theory of piecewise smooth vector fields a Sliding Shilnikov Orbit is a trajectory, in the Filippov sense, connecting a saddle focus pseudo-equilibrium to itself. Recently, it has been shown that this connection provides a chaotic dynamic without further assumptions. In this talk, we explore the dynamics of this connection and an application for biological models is presented.
References
D.D. Novaes, G. Ponce, and R. Varão, Chaos induced by sliding phenomena in Filippov systems, J. Dyn. Diff. Equat. 29 (2017), 1569-1583.
D.D. Novaes and M. A. Teixeira, Shilnikov problem in nonsmooth dynamical systems, Chaos 29 (2019), 063110.
T. Carvalho, D.D. Novaes, and L.F. Gonçalves, Sliding Shilnikov Connection in Filippov-type Predator-Prey Model, Nonlinear Dynamics, 100 (2020), 2973-2987.