ANALYTICAL CONDITIONS FOR AMPLITUDE DEATH INDUCED BY CONJUGATE VARIABLE COUPLINGS

We construct local and global conjugate variable coupled chaotic systems with an arbitrary number of identical chaotic oscillators. Amplitude death phenomena are found in these two kinds of systems. General methods are proposed to theoretically analyze conditions for amplitude death under local and global conditions, respectively. Taking the Rossler chaotic system as the oscillator unit, we apply these methods to determine the analytical conditions for amplitude death. And the transition relations between local and global coupling induced amplitude deaths are also given. All theoretical results are well confirmed by numerical simulations.