ECASisDin

In this talk, I will discuss how stochastic perturbations of Filippov differential equations, of the form \( d x_t = F(x_t) dt + \varepsilon d W_t \) , converge to a Filippov convention solution as the noise strength \( \varepsilon \) approaches zero. This is an ongoing joint work with Prof. Douglas Novaes.

In this talk I’ll summarise a few ideas in nonsmooth systems that have yet to be exploited, and some problems yet to be explained. They concern the nature of discontinuities, how we model them, and their singularities.

TBA

In this talk, we explore the simultaneous bifurcation of limit cycles in planar piecewise quadratic differential systems separated by a straight line. We will investigate how these limit cycles arise from a degenerate Hopf bifurcation at two equilibrium points in the positive and negative half-planes, as well as from an equilibrium on the separation line. All the limit cycles discussed are of small amplitude. A central focus of the presentation will be demonstrating how this bifurcation creates a novel coexistence configuration of limit cycles of type \( (3, 5, 3) \). Additionally, we will present the analytical steps proving that, in each half-plane, the maximum number of small-amplitude hyperbolic limit cycles that a quadratic vector field can have is three. Joint work with Leonardo P. C. da Cruz and Joan Torregrosa.