Detecting anomalous phase synchronization from time series

Abstract

Modeling approaches are presented for detecting an anomalous route to phase synchronization from time series of two interacting nonlinear oscillators. The anomalous transition is characterized by an enlargement of the mean frequency difference between the oscillators with an initial increase in the coupling strength. Although such a structure is common in a large class of coupled nonisochronous oscillators, prediction of the anomalous transition is nontrivial for experimental systems, whose dynamical properties are unknown. Two approaches are examined; one is a phase equational modeling of coupled limit cycle oscillators and the other is a nonlinear predictive modeling of coupled chaotic oscillators. Application to prototypical models such as two interacting predator-prey systems in both limit cycle and chaotic regimes demonstrates the capability of detecting the anomalous structure from only a few sets of time series. Experimental data from two coupled Chua circuits shows its applicability to real experimental system.

Synchronization of electrochemical oscillators with differential coupling

“…Strongly nonisochronous oscillators often form rich synchronization patterns [26][27][28][29]. For example, in pairs of asymmetrically coupled oscillators "anomalous" phase synchronization effects were reported in the form of advanced or delayed synchronization and frequency difference enhancement or inversion [25,27,30,31]; in globally coupled oscillators diffusion-induced inhomogeneity can occur in the form of periodic or quasiperiodic amplitude clusters [28]. In a previous work [32], by increasing the temperature of oscillatory Ni dissolution from 10 to 20 • C, nonisochronicity of asymmetrically coupled oscillators resulted in advanced or delayed synchronization depending on the relative frequencies of the driver and follower oscillators.…”

The emergence of synchrony behavior in weakly coupled electrochemical oscillators via a ‘metallic plate’

“…coupling via a dynamic environment) [16,17], differential coupling (wherein an oscillator gets affected by the rate of change of the other oscillator's state variables, i.e. fast/slow, rather than by the instantaneous magnitude of its state variables) [18], asymmetric coupling (that means different coupling constants) [19,20] etc. Analogously, we have explored a novel scenario wherein the correlation between two non-electrically coupled electrochemical oscillators gets enhanced (i.e.…”