Quasiperiodic perturbations of heteroclinic attractor networks
| Autor: | Antoni Guillamon, Amadeu Delshams, Gemma Huguet |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Binocular rivalry
Bistability Chaotic General Physics and Astronomy Duffing equation Dynamical Systems (math.DS) 01 natural sciences 010305 fluids & plasmas Hamiltonian system 03 medical and health sciences 0302 clinical medicine 0103 physical sciences Attractor FOS: Mathematics Sistemes hamiltonians Statistical physics Mathematics - Dynamical Systems Hamiltonian systems Mathematical Physics Attractor network Mathematics Applied Mathematics Matemàtiques i estadística [Àrees temàtiques de la UPC] Statistical and Nonlinear Physics Numerical integration Nonlinear Sciences::Chaotic Dynamics 37D45 37E99 37M05 92B05 030217 neurology & neurosurgery |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | 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 quasiperiodic perturbations. For this purpose, we present a methodology based on the separatrix map to model the dynamics close to heteroclinic networks with quasiperiodic perturbations. Our methodology unifies two different approaches, one based on Melnikov integrals and the other 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, for which we develop a suitable method based on Melnikov integrals for non-Hamiltonian systems. In both models, the perturbed system shows chaotic behavior, while dominance times achieve good agreement with gamma distributions. Moreover, the separatrix map provides a new (discrete) model for bistable perception which, in addition, replaces the numerical integration of time-continuous models and, consequently, reduces the computational cost and avoids numerical instabilities |
| Databáze: | OpenAIRE |
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