Biswadip Dey

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  Synchronization in Neuronal Oscillator Networks
  Biswadip Dey
  Mathematical analysis of synchronization in networks of neuronal oscillators provides a better understanding of neuronal ensemble behavior in the brain. Moreover, systematic means to analyze the influence of network structure and external stimulation on network synchronization have the potential to improve methods for treating synchronization-related neurological disorders (e.g. epileptic seizure, Parkinson's disease etc.). In this talk, we will investigate synchronization in networks of homogeneous FitzHugh-Nagumo (FN) oscillators interconnected via electrical gap junction couplings, and derive sufficient condition (a bound on the coupling strength) for synchronization. By using non-smooth Lyapunov functions, our approach provides an improvement over previous results. Then, by considering a FN network with heterogeneous inputs, we will demonstrate how cluster synchronization emerges out of symmetry in the interconnection graph.