Jose Mujica (Vrije Universiteit Amsterdam)
Title: Heteroclinic cycles under forced symmetry breaking: coupled oscillators, reduced dynamics, normal forms and invariant manifolds
Abstract: Networks of oscillatory units are an active area of research due to their connections with brain functions and the complex collective dynamic arising on these models. We consider a network of coupled oscillators which, in the fully symmetric case, supports a robust dissipative heteroclinic cycle between dynamically invariant sets with localised frequency synchrony. The heterocilinic connections involved in the cycle lie on invariant subspaces yield by the symmetries of the system and are caused by the presence of higher order interactions.
In this talk, we focus on what happens in this heteroclinic structure when the symmetries of the system are broken. In particular, we will discuss some partial results on how such a perturbation affects the asymptotic dynamic near saddle sets involved in the cycle. To this end, we study normal forms for the reduced dynamics obtained via a parametrisation. This will set up the stage for further numerical investigation of these global connections.
November 8th 2022, 14:00, in person (Byron beige, Byron building) and Zoom meeting
