Dynamical Analysis Of Complex Nonlinear Systems

With the progress of human society,complex nonlinear systems and complexity science are involved in more and more fields,and the research on complex nonlinear systems has become a hot research topic in various disciplines.In recent decades,as one of the main forms of complex nonlinear system,memristive neural networks have played an important role in associative memory,pattern recognition,fixed-point computing,signal processing,combination optimization,nanotechnology and other practical applications.In addition,as a typical complex nonlinear system,complex networks have a wide cross with mathematics,biology,social science,physics,computer,information science and many other disciplines,and have been applied to many fields such as economy,society,politics,military and so on.Therefore,it is very important to analyze and study the dynamic behavior of memristive neural networks and complex networks.Therefore,this thesis studies the fixed-time lag synchronization of memristive neural networks,the passivity and stability of discrete-time memristive neural networks,the exponential dissipativity of discrete-time switched complex networks with actuator saturation and parameter uncertainties.The specific research contents are as follows:1.The problem of fixed-time lag synchronization is investigated for memristive neural networks with time delays.Firstly,in the sense of Filippov solution,combined with the theories of set-valued map,differential inclusion,measurable selection,Lyapunov stability and fixed-time stability,the synchronization behavior of the system under two different control strategies are studied respectively.Secondly,criterions are established to ensure the system to achieve fixed-time lag synchronization,and the settling times of synchronization are estimated.Finally,the validity of the theoretical results is verified by numerical simulation.2.The problem of exponential stability and exponential passivity analysis are studied for discrete-time memristive neural networks with additive time-varying delays and leakage delays.In the sense of Filippov solution,combined with the theories of set-valued map,measurable selection,differential inclusion,Lyapunov stability and passivity,the exponential stability and exponential passivity of the system are studied respectively.By applying the extended matrix inequality and new weighted summation inequality,the necessary conditions for exponential stability and exponential passivity of the corresponding system are obtained.Finally,the effectiveness of obtained results is demonstrated by a numerical example.3.The problem of exponential dissipativity is investigated for discrete-time switched complex networks with parameter uncertainties and actuator saturation.Firstly,under the mode-dependent average dwell time switching,by applying the quasi-time-dependent method,the problem of(Q,S,R)-exponential dissipativity and exponential stability of closed-loop systems are investigated respectively.Secondly,under the average dwell time switching,the criterion of exponential stability and(Q,S,R)-exponential dissipativity of closed-loop systems are obtained respectively.Finally,a numerical example is given to illustrate the validity of the results.