Seminarium Wydziału Fizyki Technicznej i Matematyki Stosowanej
Prof. Fátima Drubi Vega Department of Mathematics, University of Oviedo, Spain
wygłosi wykład pt. „Coupled Systems: From Simple to Complex Dynamics”.
Abstrakt:
When working with coupled systems, it is quite common to face scenarios where the isolated systems undergo a Hopf bifurcation.
This is the case, for instance, in many coupled neuron models. Under this assumption, the appearance of additional degeneracies after the coupling may lead to Hopf-Hopf bifurcations, which are likely to become germs of complex bifurcation diagrams.
This context raises many interesting questions.
We consider a four-dimensional family of vector fields, consisting of two identical FitzHugh-Nagumo systems linearly coupled by diffusion. We classify the Hopf-Hopf singularities that appear in this coupled system and identify seven of the eleven possible
cases of Hopf-Hopf bifurcations. The bifurcation diagram of two cases reveals the emergence of quasi-periodic dynamics,
characterized by the presence of two-dimensional and three-dimensional attracting tori. We examine these specific cases in greater detail by studying the associated local bifurcations through concrete examples and presenting relevant numerical simulations.
Further explorations highlight the dynamical richness, extending beyond the local bifurcation diagrams.