Synchronization in networks of coupled dynamical systems
21 Setembro 2015 ·
- Quem: Jaap Eldering
- Onde: FGV - Praia de Botafogo, 190, sala 317
- Quando: 21 de Setembro de 2015 às 16:00h
Various systems in nature can be described by dynamical systems coupled through a network structure, for example a network of neurons or coupled oscillators. It is important to understand under which conditions such networks synchronize, since in many applications synchronization is a property that is either desired or undesirable (e.g. in epilepsy attacks).
I will introduce a mathematical model for a network of identical dynamical systems with a general “diffusion-like” coupling, i.e. a coupling that pushes connected nodes to a common state. Our main result is that when the coupling is sufficiently strong, then such a network of nodes (with general dynamics) has a stable synchronized state. Furthermore, our technique of using the dichotomy spectrum then also implies that this persists, even when the nodes are not exactly identical.
This is joint work with Tiago Pereira, Martin Rasmussen and Alexei Veneziani.
Palestrante
Jaap Eldering obtained his PhD at Utrecht University, The Netherlands in 2012. After that, he was a postdoc at Imperial College London, and since June 2015 he is a visiting researcher at PUC-Rio.
His research interests are broadly in dynamical systems and (geometric) mechanics. His PhD thesis was on normally hyperbolic invariant manifolds (in particular, on extending persistence results to noncompact manifolds in bounded geometry). Since then, he has worked on various more applied problems, such as network synchronization, biolocomotion, a particle model for fluid flow, and nonholonomic dynamics.
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