Abstract
We study relaxation oscillators with couplings that mimic excitatory chemical synapses. Such oscillator networks have been shown to synchronize quickly without time delays. We present analytic results for a pair of oscillators showing that loose synchrony occurs for a wide range of initial conditions and time delays. Simulations indicate that locally coupled networks in one and two dimensions also exhibit loose synchrony. To characterize loose synchrony we introduce a measure of synchrony, the maximum time difference. We obtain histograms of this measure for one and two dimensional oscillator networks. Also, we conjecture that there is a range of initial conditions for which the maximum time difference remains bounded as the system evolves.
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