The Traveling Chimera State In Non-locally Asymmetric Coupled Phase Oscillators

In nonlinear dynamics,the phenomenon that the output or input of an object changes between two or more independent objects through the interaction of their respective internal elements can be called coupling,and non-locally coupled is a coupled mode that decays with distance.Coupled identical phase oscillators system evolves into a spatio-temporal mode of coexistence of coherent and incoherent under certain conditions,i.e.,chimera states.In this paper,we study the traveling chimera state of one-dimensional array of non-locally asymmetric coupled phase oscillators under random initial conditions,the snapshot of phase pattern for traveling chimera state is intercepted after setting up suitable initial conditions for the system,and the differential equations of the system are resolved by using Runge-Kutta method.The moving characteristics of chimera states are observed by analyzing the quantitative relations between parameters such as complex order parameter,instantaneous angular velocity,phase change and non-locally asymmetric coupled strength.The results is confirmed by the theoretical analysis based on the Ott-Antonsen ansatz that the onedimensional non-locally asymmetric coupled phase oscillators system evolves traveling chimera state under the condition of smaller asymmetric coupling(??0.02),and its coherent cluster moves to the left,and the moving velocity ? increases with the increase of the asymmetric coupling strength ?.When the asymmetric coupling is larger(??0.02),all oscillators are synchronized and have the same angular velocity ,and a traveling wave appears.The numerical simulation matches with the simulation results.Chapter 4 constructs a non-locally coupled multigroup logistic chaotic mapping circuit by using the DSP Builder module in the Simulink function on Matlab software to achieve partial synchronization of the multigroup circuit.