Complex Dynamic Behavior Of The Dynamo Chaotic Model Driven By Jump Process

In the real world,the complex system will inevitably be subjected to all kinds of uncertain random influence of factors,and these effects are subtle or even profound for the evolution of dynamic properties of complex systems.In recent years,more and more scholars pay attention to the complex phenomena of the stochastic model in biological system,climate system,power system and material science.In this paper,by using the knowledge of stochastic analysis,stochastic differential dynamical system,Markov semigroup and jump stochastic process,we discuss the complex dynamic behavior of dynamo chaotic model driven by jump process.The main contents of this paper are as follows:In the first chapter,we will focus on the current research situation and background significance of dynamo chaotic model,related concepts,definitions,lemmas and other basic knowledge,and briefly describe the main framework structure and research content of this dissertation.In the second chapter,we mainly discusses the stationary measure and exponential ergodicity of the stochastic dynamo chaotic model driven by Lévy stochastic process.Firstly,by constructing appropriate Lyapunov function,using the knowledge of integral and differential operator,symmetric ?,Markov invariant measure of skew product flow,random dynamic system and stochastic functional analysis techniques,we proved the exponent ultimately bounded and stablity of the stochastic dynamo chaotic model driven by Lévy jump process.Secondly,By using martingale exponential inequality,Markov semigroup,invariant measure and Girsanov's theorem,we discussed the irreducibility and strong Feller properties of the transition probability of the stochastic dynamo chaotic model driven by Lévy jump process.Finally,the exponential ergodicity and spectral gap of the corresponding transfer semigroup are obtained.In the third chapter,we mainly studies the stability and bifurcation of the stochastic dynamo chaotic model driven by Poisson process.Firstly,we prove the global exponential stability of the stochastic dynamo chaotic model driven by Poisson process by ingeniously constructing the appropriate Lyapunov function and using the technique of random functional analysis.Secondly,by using the invariant measure theory,Lyapunov exponent and random dynamical system,we obtained the global exponential attractor of the stochastic dynamo chaotic model driven by Poisson process.Finally,by analyzing the long-term behavior of random attractors in the stochastic dynamo chaotic model,that is,the evolution of random attractors from single point set to random tray set,we obtained the existence conditions of random bifurcation for stochastic dynamo chaotic model.