Emergence and synchronization of a reversible core in a system of forced adaptively coupled Kuramoto oscillators

We report on the phenomenon of the emergence of mixed dynamics in a system of two adaptively coupled phase oscillators under the action of a harmonic external force. We show that in the case of mixed dynamics, oscillations in forward and reverse time become similar, especially at some specific frequencies of the external force. We demonstrate that the mixed dynamics prevents forced synchronization of a chaotic attractor. We also show that if an external force is applied to a reversible core formed in an autonomous case, the fractal dimension of the reversible core decreases. In addition, with increasing amplitude of the external force, the average distance between the chaotic attractor and the chaotic repeller on the global Poincare secant decreases almost to zero. Therefore, at the maximum intersection, we see a trajectory belonging approximately to a reversible core in the numerical simulation.

Automated summary

The study investigates the emergence of mixed dynamics in a system of adaptively coupled phase oscillators under the influence of an external force, which prevents forced synchronization of chaotic attractors and affects the fractal dimension of reversible cores. The average distance between chaotic attractors and repellers decreases with increasing external force amplitude, leading to trajectories belonging approximately to reversible cores in numerical simulations at maximum intersection.