Novel Synchronization of Pulse-Coupled Oscillators on Time-Varying Networks

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In this article I investigate the novel synchronization behaviors of evolving pulse-coupled oscillator networks. Unlike previous models, the time-varying mechanism is inspired by neural network development, where seldom used links die out while heavily used ones get strengthened. Even small network with all-to-all connected topology can have exotic dynamics under this circumstance. The oscillators can coevolve with the network, and finally form a co-synchronized pair. Or if we only allow a fraction of oscillators to send pulses every time, the oscillators can synchronize with the network remain chaotic.