Antiphase Synchronization in Environmentally coupled Rossler Oscillators

TL;DR

This paper investigates how Rossler oscillators coupled via a dynamic environment can achieve antiphase synchronization, with phase relationships and transitions characterized by Lyapunov exponents in both periodic and chaotic regimes.

Contribution

It demonstrates the emergence of antiphase synchronization in environmentally coupled Rossler oscillators and analyzes phase distribution and Lyapunov spectrum transitions.

Findings

Oscillators synchronize in antiphase with phase lag of 2π/n.

Transition marked by (n-1) zero Lyapunov exponents becoming negative.

Chaotic systems can become periodic and synchronize in antiphase with sufficient coupling.

Abstract

We study the manifestation of antiphase synchronization in a system of n Rossler Oscillators coupled through a dynamic environment. When the feedback from system to environment is positive (negative) and that from environment to system is negative (positive), the oscillators enter into a state of anti phase synchronization both in periodic and chaotic regimes. Their phases are found to be uniformly distributed over 2$pi$, with a phase lag of 2$pi$ /n between neighbors as is evident from the similarity function and the phase plots. The transition to anti phase synchronization is marked by the crossover of (n-1) zero Lyapunov Exponents to negative values. If the systems are individually in chaotic phase, with strong enough coupling they end up in periodic states which are in antiphase synchronization