Study On Amplitude Death And Synchronization And Anti-synchronization Of Chaotic Systems

In this paper,law of amplitude death for two identical or different dynamical systems was explored,which would be extended to amplitude death of collective oscillations with an arbitrary number of identical dynamical systems,meanwhile,the phenomena of synchronization and anti-synchronization are also studied.Combineding with theoretical analysis and numerical calculation,necessary and sufficient conditions for amplitude death or synchronization and anti-synchronization in coupled chaotic systems was obtained,and circuit experiments(or circuit simulations) have obtained sufficient and correct results which demonstrate the methods we proposed.Based on conjugate-variable coupling,we have studied on amplitude death of coupled dynamical systems with two identical chaotic oscillators,two mismatch chaotic oscillators and two different chaotic oscillators respectively.We obtained the analytical conditions for amplitude death through linear stability theory,and observed the phenomena via numerical simulation and circuit experiments.Amplitude death in both global and local coupling systems,which coupled with a large number of identical chaotic oscillators,was studied based on non-time-delay variables' conjugate coupling.New coupling scheme was proposed,and analytical conditions for amplitude death were achived through theoretical analysis.Also,transition relations between different styles of coupling were deeply analysis,and analytical conditions for amplitude death in local coupling(or multiple neighbor coupling) were expanded.Circuits for coupling systems with particular parameters were designed,which are connected with adjustable number of sub-circuits,and the results of numerical simulation agree well with that of circuit experiments.Finally,we consider the synchronization and anti-synchronization coexistence in coupled chaotic systems.Theoretical conditions and ways of Variable coupling wre proposed,and analytical conditions were obtained by numerical calculations.Also,we have observed both synchronization and anti-synchronization phenomena in special Chua's circuit.In addition,taking the potential applications of time-delayed system into account, we have further studied synchronization and anti-synchronization coexistence in time-delayed chaotic systems,and received consistent results in theoretical analysis, numerical calculations and circuit experiments.The theoretic and numeric methods are integrated closely in this paper.The results about amplitude death,synchronization and anti-synchronization,provide important theoretical and experimental foundation for practical application.