We study the dynamics of coupled nonlinear oscillators and investigate the conditions under which linear coupling of these oscillators leads to either synchronization or desynchronization of the relative phases of oscillations. This question has been previously addressed for infinitesimally small Limit cycle oscillators, i.e., for oscillators in the vicinity of a Hopf bifurcation. In the present paper, we generalize these results by studying limit cycle oscillators with finite size. This is achieved by expanding the dynamics of the nonlinear dynamical systems in terms of deviations from a circular limit cycle of finite size. Taking into account only lowest-order expansion terms, we analytically derive a condition for desynchronization which goes beyond the Benjamin-Feir criterion obtained in the framework of the third-order Ginzburg-Landau theory.
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