Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico

Fecha : 26 de mayo de 2022
Hora  : 11:30
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)

José Pablo Mujica Torres

(Vrije Universiteit Amsterdam, Países Bajos)

Resumen

It is well known that invariant manifolds of invariant objects (e.g. equilibria or periodic orbits) constitute the skeleton of a dynamical system. They provide boundaries between regions on phase space with qualitatively different behaviour, and their interactions give rise to changes in the configuration of a system by means of global bifurcations; typical examples that arise in applications are homoclinic and heteroclinic bifurcations. In this talk we will discuss some ideas related to the numerical computation of invariant manifolds as a family of orbit segments that are solution to a suitable boundary-value-problem. We will use the computed manifolds to study the overall dynamics of a system, and track their interactions to describe the underlying geometric mechanisms that create complex dynamics. As a first example we will show how this ideas can be used in the context of slow-fast systems, in which a global invariant manifold can interact with a slow manifold creating sustained dynamics in the form of mixed- mode oscillations. Secondly, we will apply some of this ideas in the context of a network of coupled oscillators to study heteroclinic cycles undergoing forced symmetry breaking.