title: Synchronization in heterogeneous FitzHugh-Nagumo networks with hierarchical architecture.
abstract: We study synchronization in heterogeneous FitzHugh-Nagumo networks. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. Here we develop a controller to counteract the impact of these heterogeneities. We first analyze the stability of the equilibrium point in a ring network of heterogeneous nodes. We then derive a sufficient condition for synchronization in the absence of control. Based on these results we derive the controller providing synchronization for parameter values where synchronization without control is absent. We demonstrate our results in networks with different topologies. Particular attention is given to hierarchical (fractal) topologies, which are relevant for the architecture of the brain.
authors: Saint Petersburg State University, St. Petersburg, Russia.|ITMO University, St. Petersburg, Russia.|Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoy Ave, 61, Vasilievsky Ostrov, St. Petersburg 199178, Russia.
authors: S A
authors: SA
authors: Plotnikov
authors: Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany.
authors: J
authors: J
authors: Lehnert
authors: Saint Petersburg State University, St. Petersburg, Russia.|ITMO University, St. Petersburg, Russia.|Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoy Ave, 61, Vasilievsky Ostrov, St. Petersburg 199178, Russia.
authors: A L
authors: AL
authors: Fradkov
authors: Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany.
authors: E
authors: E
authors: Schöll