The influence of nonisochronism on mixed dynamics in a system of two adaptively coupled rotators

Abstract

We study the influence of nonisochronism on the phenomenon of mixed dynamics in a system of two adaptively coupled rotators. We manifest that nonisochronism can either cause or destroy mixed dynamics. We show that the phenomenon is robust and declare its domain of existence. We reveal that at the part of the boundary of the parameter domain where mixed dynamics takes place, an attractor–repeller bifurcation happens which is an analogue of the saddle–node bifurcation. We denote that the modulus of the sum of the Lyapunov exponents of the chaotic attractor is lower at the parameter values corresponding to mixed dynamics than in other parameter domains, and its lowest value matches with the attractor–repeller bifurcation, when the system resembles a conservative one more strongly than in the isochronous case of mixed dynamics. We reveal that with growing the amplitude of nonisochronous term, the Kantorovich–Rubinstein–Wasserstein distance between the attractor and the repeller gets lower, so they become more alike, approaching the form of the reversible core.