Dynamics Of Spiral Wave Chimeras Under The Control Of External Fields

Chimera state is a kind of spatial and temporal pattern with synchronous and asynchronous coexistence.It exists in many complex systems in nature and plays an important role in the research of physical,chemical and life science systems.Spiral wave chimera state is the combination of spiral wave and chimera state,which is a typical form of chimera in two-dimensional space.It is a hot topic in nonlinear dynamics and complex system research.At present,researches on chimera state focus more on discovering the existence of chimera state,exploring different types of chimera state and the mechanism of their formation in different systems.Since chimera state is closely related to the realization of some functions in living systems,how to regulate chimera state is a very important and basic problem.At present,most of the work related to chimera state regulation is limited to one-dimensional system,and we know very little related to spiral wave chimera state regulation in two-dimensional system.This thesis focuses on the dynamic behavior of spiral wave chimera state under the control of external field,and got some useful results.The structure of the thesis is as follows:Chapter 1 introduces the research background of spiral wave pattern and chimera state,focuses on the development and research progress of spiral wave chimera state,and expounds the motivation of our research.In chapter 2,the regulation of periodic field and direct current field on stable single spiral wave chimera states is discussed,found the dynamic phenomenon of drift will occur in both fields,and in the course of the drift,the nature of chimera state is still intact,asynchronous nucleus remained stable,and the speed and direction of drift are determined by the parameters of the external field and the chirality of the spiral wave chimera state.The third chapter mainly studies when several stable spiral wave chimera states coexist,chiral symmetry breaking and chiral selection will occur by applying a circular polarization electric field(CPEF).Through analysis,we found that the phenomenon is the result of different chirality spiral waves chimera to pull to the different frequency response of CPEF,by adjusting the frequency and chirality of the CPEF,we can control the chirality of final existence state of spiral wave chimera.More precisely,when the field frequency is less than the system frequency,eventually chirality of the existence and the chirality of CPEF is the same,if the external field frequency is greater than the system frequency,the existing chirality is opposite to that of CPEF.Then we systematically study the frequency synchronization of CPEF,and propose a qualitative explanation for the phase-locking phenomenon and chiral selection behavior caused by the external field based on the response function theory and the final Adler phase equation.We summarize the research results and make a outlook in chapter 4.