Dia: Dimecres, 21 de novembre de 2018
Lloc: Aula T1 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Gemma Huguet, Universitat Politècnica de Catalunya
Títol: Quasi-periodic perturbations of heteroclinic attractor networks
Resum: We consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that Gamma distributions of dominance times observed experimentally in binocular rivalry and other forms of bistable perception, commonly explained by means of noise in the models, can be achieved with quasi-periodic perturbations. For this purpose, we present a methodology based on the separatrix map to model the dynamics close to heteroclinic networks with quasi-periodic perturbations. Our methodology considers two different approaches, one based on Melnikov integrals and another one based on variational equations. We apply it to two models: first, to the Duffing equation, which comes from the perturbation of a Hamiltonian system and, second, to a heteroclinic attractor network for binocular rivalry. In both models, the perturbed system shows chaotic behavior while dominance times achieve good agreement with Gamma distributions. Moreover, the separatrix map provides a discrete model for bistable perception. This is joint work with A. Delshams and A. Guillamon
Last updated: Thu Nov 15 14:34:08 2018