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Synchronization in a population of oscillators with hyperbolic chaotic phasesis studied for two models. One is based on the Kuramoto dynamics of the phaseoscillators and on the Bernoulli map applied to these phases. This systempossesses an Ott-Antonsen invariant manifold, allowing for a derivation of amap for the evolution of the complex order parameter. Beyond a criticalcoupling strength, this model demonstrates bistability synchrony-disorder.Another model is based on the coupled autonomous oscillators with hyperbolicchaotic strange attractors of Smale-Williams type. Here a disorderedasynchronous state at small coupling strengths, and a completely synchronousstate at large couplings are observed. Intermediate regimes are characterizedby different levels of complexity of the global order parameter dynamics.

Synchronization of oscillators with hyperbolic chaotic phases