Research On The Mechanism Of Death Control In Nonlinear Systemsbased On Continuous And Discontinuous Coupling

Death is a kind of common cluster dynamics phenomenon in coupled nonlinear systems,which mainly has two manifestations:amplitude death?AD?and oscillation death?OD?.AD and OD are deeply researched by many researchers and also the hot topic in nonlineardynamics field due to they play an important role in the practical applications of biological,chemical,medical and engineering vibration damping.However,the intrinsic nonlinear factors and the external coupling modes are recognized as the main reasonsfor the phenomenon of death dynamics.Therefore,it is a great significance tofurther research the phenomenon of AD and OD.In this thesis,we mainly study the effects of "continuous coupling" and "discontinuous coupling" on the dynamics mechanism of AD in Landau-Stuart oscillator systems.The research backgrounds,development directions and research status of AD and OD are introduced detailedly inthe front section of thesis,and then the basic theories of nonlinear dynamics and the common nonlinear oscillator models are also introduced briefly.With the help of numerical calculation and data graphic analysis,three aspects are mainly studied:?1?the influence of the continuous coupling on AD of Landau-Stuart oscillator systems.?2?the effect of the discontinuous coupling on AD of Landau-Stuart oscillator system.?3?Based on the analysis of the AD phenomenon of limit cycle oscillator systems,the influence of discontinuous coupling on AD of Rossler chaotic oscillator systemsare also extended and researched.The results show that when the coupling strength is continuously changed,due to the effect of parameters and the inherent characteristics of various coupling modes?including parameter mismatch,time delay,conjugate coupling,dynamic coupling,linear enhancement coupling,nonlinear coupling and diffusion coupling?,the AD phenomenon of coupled Landau-Stuart oscillator systems will appear in a certain range,and also the only one coupling strength can be found,which makes the largest Lyapunov exponent ?_max minimum.When the coupled Landau-Stuart oscillator systems are coupled with discontinuous coupling,ifthe period T and switching frequencya have a appropriate value,the AD phenomenon can be also induced,and the size of the dead regions have a positive correlation with the frequency mismatch ?_?.Besides,it is also found that the results of regularity and universality are similar to the limit cycle oscillator systems,when the chaotic Rossler oscillator systems arealso coupled by the discontinuous coupling.Through three aspects of the research on the dynamic systemsabove,we are convinced that there must be more dynamic phenomena in the coupled oscillator systems,and we expect that the relevant research contents can get more practical applications,and the research results can provide theoretical help and guidance for related applications.