Study On The Dynamic Mechanism Of Oscillation Quenching In Coupled Nonlinear Systems

Oscillation quenching is a kind of common cluster dynamics phenomenon in coupled nonlinear systems which exhibit oscillation suppression of coupled subsystem due to some factors.It mainly has two manifestations: amplitude death(AD)and oscillation death(OD),which plays an important role in biological,chemical,vibration suppression in engineering and other practical systems.However,the intrinsic nonlinear factors and the external coupling modes are recognized as the main reasons for the phenomenon of oscillation quenching.Therefore,it is a great significance to research the phenomenon of oscillation quenching,as well as AD and OD.In this thesis,we mainly investigate two different quenching phenomena,i.e.,AD and OD and their inner mechanism and mutual transformation processes.The thesis firstly introduces some related phenomena,development status,application scenarios about chaos and the phenomenon of oscillation quenching and synchronization in coupled nonlinear systems,and then the basic theories of nonlinear dynamics are also introduced briefly.Based on two aspects of the intrinsic nonlinear factors and the external coupling modes,serveral questions are explored as following,(1)the influences of oscillators' s natural frequency(intrinsic factor)on the region of AD and OD in coupled Landau-Stuart systems,(2)the effects of dual-channel coupling(external coupling mode)on the phenomenon of oscillation quenching in coupled nonlinear systems,(3)the influences of an additional repulsive or attractive coupling channel on the formation mechanism of AD and OD and their mutual transformation.The results show that the phenomenon of oscillation quenching are closely related to the natural frequency of oscillators in all kinds of single channel coupled systems(either identical and nonidentical systems,or diffusive coupling and conjugate coupling systems).The smaller(larger)the natural frequency of coupled oscillators are,the easier for the coupled systems get to OD(AD).However,the dynamic behavior and the region distribution of amplitude death have no links with the value of natural frequency in dual-channel diffusivly coupled systems,while the region of amplitude death for dual-channel conjugately coupled systems are positively correlated with the natural frequency.The additional repulsive coupling channel in the formally single channel system tends to shrink the AD domain while enlarge the OD domain,however,an additional attractive coupling acts inversely.Meanwhile,the original transitions from AD to OD of coupled systems are replaced by transitions from OS(oscillation state)to AD or from OS to OD with the effects of different frequency mismatches and dual-channel coupling.Our researches,namely,the AD and OD dynamics regimes,and their transition processes in coupled oscillators are explored numerically and theoretically.It is expected that the results are helpful to better understand and control the formation of AD and OD and their transition processes,and also provid a fundamental theoretical basis for chaos control,physical application and bioengineering and other fields.