Abstract
Phenomena of synchronization are studied for systems of infinitely many van der Pol type oscillators which have symmetrically distributed native frequencies and are coupled with each other via mean-field interactions of linear form. Totally synchronized (TS), quenched (Q), partially synchronized (PS), and totally dissynchronized (NS) states are shown to appear depending on the values of the coupling strength and the width of the native frequency distribution of the systems. The phase boundary between the TS and Q phases for the systems with strong couplings is rigorously determined on the basis of mean-field theoretical analysis involving the concept of order parameter.
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