Antiphase Synchronization in Environmentally coupled Rossler Oscillators

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