Some Properties Of Dynamical Systems With Variable Parameters

The core issues of dynamical system are the asymptotic nature of the orbit or topological structure of the orbit, but only those with the orbit of the properities of recovery are important. Therefore, the study of the properities of recovery constitutes the foundation of dynamical system. At the same time, topological transitivity, sensitive dependence on initial value and chaos reflect the complexity of the system from different aspects. This thesis promotes the original reply, topological transitivity, sensitive dependence on initial value and chaos on the basis of them and extends the scope of dynamical system, which better reflect the intrinsic nature of the system and lay a theoretical foundation for the future application.The contents of this thesis are as follow:Chapter 1 briefly introduces the development process of dynamical system, the background and the main results of this thesis.Chapter 2 puts forward the definition of subsystem on the basis of variable parameters dynamical system. In the above dynamical system, it gives out the definitions of periodic points, recovering pionts,ω-limit points and almonst periodic points of a sequence of maps. Meanwhile, it preliminary researches the properities of the above definitions and the relationships between them.Chapter 3, in the above system, gives out the definitions of topological new transitivity, topological transitivity, topological strong transitivity and topological conjugate of a sequence of maps, studies basic properties of the above topological conjugate, and obtains some main results, proves topological new transitivity and topological transitivity are equivalent u-under a compact metric space, a sequence of full maps and interchangeable with each other, and that some conclusions associated with topological conjugate.In Chapter 4, in the above system, the definitions of sensitive dependence on initial value, strong sensitive dependence on initial value and chaos set of a sequence of maps are put forward; Meanwhile, sensitive dependence on initial value of a sequence of maps is promited, and the concept of N - sensitive factor is also proposed; That at the local connected space λ₂/(N-1) is a N—sensitive factor, and a chaotic map containing strong sensitive dependence on initial value of a sequence of maps is proved.This thesis finally summarizes the main results and innovation, as well as some further research.