Study On Synchronization Of Several Coupled Non-identical Rossler Oscillators System

Complex systems in reality can often be simulated by coupled nonlinear oscillators,and limit cycles(periodic oscillators)or chaotic oscillators have been used to describe the dynamic behavior of a complex system.Rossler model is a typical model to study the dynamical behaviors of coupled chaotic oscillators,such as synchronization and oscillation death.In addition,recent studies have shown that coupled systems can also be used to study some interesting dynamic phenomena related to information processing in biological organism and quadruped locomotion gaits.In this paper,we consider the non-identical Rossler oscillator system,and mainly analyze the model of chain and star coupling.In a chain system coupled with several oscillators,changing the parameters of frequency mismatches and the attractive coupling strength,we observe many different spatial patterns,such as complete synchronization,in-phase synchronization,anti-phase synchronization of periodic states and chaotic states,and oscillation death.Furthermore,we traverse the control parameters of the system.Along the direction of increasing frequency mismatch between the central oscillator and the symmetric edge oscillators,the transition processes of these spatial-temporal patterns of the chaotic system are from incoherent states,via phase synchronization by periodic states with phase difference of 2?/N,to the fully synchronous state with zero phase difference,and then in the case of larger mismatch parameters into the state of oscillation death(note:The amplitudes of the central oscillator and the edge oscillators are at different positions near zero).Secondly,the effects of frequency mismatch and coupling strength on the star network with N+1 oscillators are investigated.When the frequency mismatch is large,in the range of periodic states,the oscillation frequency of the central oscillator is N times that of the edge oscillators,and the N edge oscillators are uniformly distributed over 2?,when the frequency mismatch is small,the double-frequency oscillation based on the envelope of time series is observed,which shows that the phase of the edge oscillators is close,and the envelope of the center oscillator is N times of the envelope of the edge oscillators.The phenomenon of double-frequency oscillation found in the chaotic system with single-variable diffusion-attraction coupling can be helpful for the following theoretical study and experimental investigation.