Weak-winner phase synchronization: a curious case of weak interactions

We report the observation of a nontrivial emergent state in a chain of nonidentical, heterogeneously coupled oscillators where a set of weakly coupled oscillators becomes phase synchronized while the strongly coupled ones remain drifting. This intriguing “weak-winner” synchronization phenomenon can be explained by the interplay between nonisochronicity and the natural frequency of the oscillator, as coupling strength is varied. Furthermore, we present sufficient conditions under which the weak-winner phase synchronization can occur for limit cycles as well as chaotic oscillators. Employing a model system from ecology as well as a paradigmatic model from physics, we demonstrate that this phenomenon is a generic feature for a large class of coupled oscillator systems. The realization of this peculiar, yet quite generic weak-winner dynamics can have far-reaching consequences in a wide range of scientific disciplines that deal with the phenomenon of phase synchronization, including synchronization of networks. Our results also highlight the role of nonisochronicity (shear) as a fundamental feature of an oscillator in shaping emergent dynamical patterns in complex networks.