On the intersection of a chaotic attractor and a chaotic repeller in the system of two adaptively coupled phase oscillators

Abstract

We report on the phenomenon of intersection of a chaotic attractor and a chaotic repeller in a system of two adaptively coupled phase oscillators. This is a feature of the presence of the so-called mixed dynamics, which is a new type of chaos characterized by the fundamental inseparability of conservative and dissipative behavior. The considered system is the first example of a time-irreversible system in which this type of dynamics is observed. We show that a crucial factor in this effect is the detuning of the natural frequencies of phase oscillators.