Abstract
Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses an Ott-Antonsen invariant manifold, allowing for a derivation of a map for the evolution of the complex order parameter. Beyond a critical coupling strength, this model demonstrates bistability synchrony-disorder. Another model is based on the coupled autonomous oscillators with hyperbolic chaotic strange attractors of Smale-Williams type. Here a disordered asynchronous state at small coupling strengths, and a completely synchronous state at large couplings are observed. Intermediate regimes are characterized by different levels of complexity of the global order parameter dynamics.
Highlights
Synchronization of chaotic oscillators has many aspects [1], one generally distinguishes complete, generalized, and phase synchronization
Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models
Intermediate regimes are characterized by different levels of complexity of the global order parameter dynamics
Summary
Synchronization of chaotic oscillators has many aspects [1], one generally distinguishes complete, generalized, and phase synchronization. Kuznetsov constructed a physical model of an oscillator with a chaotic phase In this construction, the process has amplitude modulation, and at each period of modulation the phase experience a doubling map. We construct a rather abstract model, where phase chaos and synchronizing interactions are separated in time (Section II). The process consists of two epochs: in one epoch phase oscillators interact according to the Kuramoto global coupling scheme, and in another epoch the phases undergo a chaotic Bernoulli map. This model demonstrates, for certain values of parameters, a bistability between a desynchronized and a synchronized states. This system demonstrates a rather reach behavior with asynchronous, completely synchronous, and complex partially synchronous states
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