Yumei Zhai

Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic Rössler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.

Characteristics of Cluster Formation in a Population of Globally Coupled Electrochemical Oscillators: An Experiment-Based Phase Model Approach

We show that cluster formation in interacting oscillators can be characterized using phase models that are developed from direct experiments with a single oscillator. One- and two-cluster states are analyzed in the phase model; the description is verified in independent experiments in sets of chemical oscillators. The experiment-based model properly describes the occurrence of one- and two-clusters; in addition, it is shown that the most stable two-cluster state exists with a balanced configuration.

Phase Synchronization in Populations of Chaotic Electrochemical Oscillators

Experiments on the collective behavior and phase synchronization of weakly coupled populations of non‐identical chaotic electrochemical oscillators are described. Without added coupling no deviation from the law of large numbers of the mean field is observed with increasing system size. Deviations do arise with very weak global or short‐range coupling; large, irregular and periodic mean field oscillations occur along with (partial) phase synchronization of the elements. The transition to phase synchronization with increasing global coupling strength is analyzed using Kuramoto’s order parameter and a comparison is made between the synchronization properties of periodic and phase coherent chaotic oscillators. Finally, the constructive effect of noise on the phase synchronization of the chaotic oscillators is demonstrated: at an optimal noise intensity an increased measure of phase synchronization is obtained.