Phase Desynchronization in Pulse-Coupled Oscillator Networks: A New Algorithm and Approach

In this thesis, we present a novel approach for achieving phase desynchronization in a pulse-coupled oscillator network. Ensuring phase desynchronization is a difficult problem, and existing results are constrained to a completely interconnected network and a fixed number of oscillators. Our approach is more robust than previous approaches, removing the constraint of a fixed number of oscillators. The removal of this constraint is significant because it allows the network to receive and drop nodes freely without any change to the phase update strategy. Also, to our knowledge, our approach is the first to prove the convergence to the desynchronized state for a topology that is more general than the all-to-all topology. More specifically, our approach is applicable to any circulant and symmetric network topology, including the circulant symmetric ring topology. Rigorous mathematical proofs are provided to support the result that any circulant symmetric network with ordered phases under our proposed algorithm will converge to uniform phase desynchronization. Simulation results are presented to demonstrate the algorithm's performance, as well as experimental results on a physical system to further illustrate applications of pulse-coupled oscillator networks.