Sync: The Emerging Science of Spontaneous Order
Sync: The Emerging Science of Spontaneous Order
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Sufficient conditions for the synchronization of coupled Lienard-type oscillators are investigated via averaging technique. The coupling considered here is fixed, nonsymmetric, and nonlinear. Under the assumption that the interconnection topology defines a connected graph, it is shown that the solutions of oscillators converge arbitrarily close to each other, starting from initial conditions arbitrarily far apart, provided that the frequency of oscillations is large enough and the initial phases of oscillators all lie in an open semicircle. It is also shown that the nearly-synchronized oscillations always take place around some fixed magnitude independent of the initial conditions and the coupling functions.