Coupling Systems for a New Type of Phase Synchronization

Florin D Grosu,Adrian Bîrzu,Ioan Grosu,Anca Lazar

doi:10.1155/2016/3574029

Abstract

Using the usual phase in plane, we propose a general method to design coupling between systems that will exhibit phase synchronization. Numerical results are shown for Lorenz systems. Phase synchronization and antiphase synchronization are equally probable depending on initial conditions. A new network with Lorenz phase synchronized system is obtained.

Highlights

Nonlinear dynamics brought to light the rich dynamics of nonlinear systems including chaotic behavior
We report here that we did not find coupling terms for Rössler by simple eye inspection as we obtained for Lorenz system
Phase is not calculated effectively but a coupling is searched which assures that the two current phases are equal

Summary

Introduction

Nonlinear dynamics brought to light the rich dynamics of nonlinear systems including chaotic behavior. By coupling two nonlinear systems a new nonlinear system with an increased dimension and richer dynamics is obtained. Many results on PS are observed for chaotic attractors with rather coherent phase dynamics [1, 2]. By using the usual definition of phase in plane we deduce a system that governs the dynamics of the phase differences. Coupling for two Lorenz systems suggests an all-to-all coupling for a network of PS and antiphase synchronized (APS) systems. Such a network can have different outputs depending on initial conditions.

Theory

Phase Synchronized Lorenz Systems

Discussions

Findings

Conclusions