Nature of synchronization transitions in random networks of coupled oscillators

Abstract

We consider a system of phase oscillators with random intrinsic frequencies coupled through sparse random networks, and investigate how the connectivity disorder affects the nature of collective synchronization transitions. Various distribution types of intrinsic frequencies are considered: uniform, unimodal, and bimodal distribution. We employ a heterogeneous mean-field approximation based on the annealed networks and also perform numerical simulations on the quenched Erdos-Renyi networks. We find that the connectivity disorder drastically changes the nature of the synchronization transitions. In particular, the quenched randomness completely wipes away the diversity of the transition nature and only a continuous transition appears with the same mean-field exponent for all types of frequency distributions. The physical origin of this unexpected result is discussed.

9 pages

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• Driven synchronization in random networks of oscillators
• Critical dynamics of the Kuramoto model on sparse random networks
• First-order like phase transition induced by quenched coupling disorder
• Collective excitability in highly diluted networks of rotators
• Validity of annealed approximation in a high-dimensional system
• Universality of critical dynamics on a complex network
• Analytical foundation for adversarial synchronization control in oscillator networks
• Noise-induced synchronization in the Kuramoto model on finite 2D lattice