Chimera States In Fitzhugh-Nagumo Model

In real life,many phenomena are related with the collective dynamics of complex networks.Complex networks can be abstracted as a system made up of a network of nodes who are connected in a certain way.Recently,the field of complex network has been fully developed,and synchronization on complex networks has been a hot topic.In 2002,Kuramoto et al.discovered an interesting phenomenon in the study of one dimensional nonlocal coupled Ginzbin-Landau phase oscillator system.Oscillators in the system are divided into coherent and incoherent regions in space.For the oscillators in the coherent region,the effective frequency keeps the same value,while the effective frequency of the oscillators in the incoherent region is distributed on a smooth curve.Later,Abrams and Strogatz called this phenomenon chimera state by using the characteristics of chimera in Greek mythology.Recent studies show that chimera state can be found not only in phase oscillators,but also in inertial oscillators,discrete chaotic system and so on.For the FHN system on a single layer network,the values of the coupling strength and the coupling radius determine the numbers of clusters of chimera states.Later,when the FHN oscillator in the system is in an excitable state,the external noise induces the oscillator in the system to be excited and oscillated,and a phenomenon named coherence resonance chimera is observed.In this paper,we investigate bipartite networks of nonlocally coupled FitzHugh-Nagumo oscillators in which the units are allocated evenly to two layers and FHN units interact with each other only when they are in different layers.We report the existence of chimera states in bipartite networks.Due to the interplay between chimera states in the two layers,many types of chimera states such as in-phase chimera states,antiphase chimera states,and out-of-phase chimera states are classified.Stability diagrams of several typical chimera states are explored in the plane of coupling strength and the coupling radius,which show strong multistability of chimera states.Finally,we have summarized the work of this article,and put forward the prospect of the work that can be continued.