Abstract
A general scheme is presented for the theoretical treatment of self-synchronization of many-body oscillators with variable amplitudes, close to harmonic ones with small nonlinearity and dissipative interactions, in the presence of external noises and a native frequency distribution. Applications of the theory are given to interacting van der Pol oscillators with various frequency distributions. The critical condition which leads to a nonvanishing order parameter is studied in detail. It turns out that the synchronization is described in terms of two kinds of bifurcation mechanism, mechanical and thermal ones. New strong slaving emerges in the case of the mechanical bifurcation. Multifarious dependences of the order parameter on the width of native frequency distribution appears in some cases because of the presence of these two bifurcation mechanisms. However, only one bifurcation of Landau type is observable since hybridization occurs when the two mechanisms coexist.
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