The Research On Clustered Chimera States And Synchronization Of Identical Nonlocal Coupled Oscillators

Chimera state is a spatiotemporal dynamical behavior that includes a synchronous oscillator region and an asynchronous oscillator region.It is difficult to capture because of its sensitivity to initial conditions and its short "survival time".Therefore,it has aroused the interest of many scholars.With the in-depth study of chimera states,the dynamic characteristics of chimera states have become more and more abundant.In this paper,we adopt two boundary conditions and two initial conditions,as well as suitable coupling ranges and phase shift parameters,clustered chimera states are found in non-local phase coupled oscillator systems.Among them,firstly,under natural boundary conditions,the system presented a more stable singularity of multiple clusters,while synchronous clusters in the chimeras under periodic boundary conditions exhibit a moving characteristic,and the moving speed of the synchronous clusters varies with the size of the system.The speed of the traveling four-cluster chimera states exponentially decreases to the increment of system size which lead to almost stable four-cluster chimera state for large system size.Considering the size effect,the Ott-Antonsen analysis method was used to reproduce the spatiotemporal dynamics of the chimera states.Finally,with the help of DSP Builder interaction software,the logistic mapping equations are implemented in simulink,and multiple two sets of interacting digital circuits and 32 digital circuits of periodic non-local coupling equations are built to achieve global synchronization and partial synchronization.