Igor Belykh

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  Dynamics of stochastically switching networks: windows of opportunity
  Igor Belykh
  In many biological networks, the individual nodes composing the network communicate via short on-off stochastic interactions. Pulse-coupled neuronal networks and ecological metapopulations with sporadic dispersal are important examples. In this talk, we present a general rigorous theory of stochastically switched dynamical networks and apply rigorous mathematical techniques to investigate the interplay between overall system dynamics and the stochastic switching process. If the switching time is fast, with respect to the characteristic time of the individual node dynamics, we expect the switching network to follow the averaged system where the dynamical law is given by the expectation of the stochastic variables. However, there are exceptions, especially in multistable networks where the trajectory may escape to another (wrong) attractor with small probability. Using the Lyapunov function method, we derive explicit bounds for these probabilities and relate them to the switching frequency and intrinsic parameters. Going beyond fast switching, we consider ecological networks and reveal an unexpected range of intermediate switching frequencies where synchronization becomes stable in a network which switches between two nonsynchronous dynamics.