Study On Chimera States In A Ring Of Coupled Oscillators

In recent years,certain research groups have found the "chimera state" behavior in the identical Kuramoto model,where some of the oscillators are synchronized,while other oscillators are asynchronous.This collective behavior has been named "chimera state",it has also been regarded as peculiar to non-locally coupled oscillator system.Chimera states can also be applied to explain the phenomenon of unihemispheric sleep in biology,that many creatures sleep with only half their brain at a time,while the other half is awake.Abrams et al.use the simplest system of Kuramoto model to explain this phenomenon,they use two oscillator systems to analog two half brains.This paper focuses on Kuramoto model,mainly researching the synchronization behaviors in non-locally coupled oscillator systems.Firstly,chimera state appeared in non-locally coupled oscillators with certain initial conditions and parameters,so we further explored and summarized more general initial conditions of chimera state.Then a second order coupling term is added to the original Kuramoto model to further explore the influences of the second order term on the collective behaviors of oscillators.We discoveried a new kind of single-clustered chimera state in which oscillators have two different phase and phase difference is ?/2;while in the same parameters but with different initial conditions,the forms of chimera states varied.We also find multi-clustered chimera state on conditions of different parameters.At the same time,we also tried to explain these phenomena using Ott-Antonse method.Secondly,based on the pre-work of Abrams et al,we further studied another Kuramoto model:a pair of oscillator populations in which coupling within each population and coupling between two populations existed simultaneously.We extended two identical subsystems to two different subsystems in which the way of internal coupling connections of two subsystems is different.Oscillators in one system coupled only with some neighborhoods within the system,while oscillators in the other system coupled with all other oscillators within the system,oscillators in one system are globally coupled with oscillators in the other system.Our study found that with the changes of the degree of oscillators in one subsystem,the system presents a rich dynamical phenomena.