Biomedical subjects
Publications and source records attributed to A S Pikovsky.
We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.
Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.
In a simple coupled-map system, we show that the desynchronization of the chaotic attractor occurs through a series of Hopf bifurcations. As a result of the accumulation of these processes, the blowout bifurcation of this coupled map system is a new kind of Hopf bifurcation from a chaotic attractor. Riddling, bubbling, and characters of this particular manifestation of Hopf bifurcation from a chaotic attractor are studied in this paper.