Dynamic Traits Under The Strong Uniform Convergence Of The Genetic And Hybrid Systems

In the late 19th- and early 20th-century,Poincaréand others brought forward the concept of dynamical systems from the study of classical mechanics and qualitative theory of differential equations.Subsequently,Birkholf published his famous Dynamical Systems in 1927 and dynamical systems developed rapidly as a systematic subject.It is well-known that uniformly convergent dynamical systems and composite dynamical systems are two important dynamical systems.If we could have a clear understanding of the relationship of dynamical behaviors between the continuous mapping sequences {f_i} and the limit mapping f,also dynamical systems(X,f),(X,g) and dynamical systems(X,fog),then we could describe dynamical behaviors of the limit mapping f through dynamical behaviors of the continuous mapping sequences {f_i},and describe dynamical behaviors of dynamical systems(X,fog) through dynamical behaviors of dynamical systems (X,f),(X,g).This offers us a feasible way to investigate general dynamical systems.In this paper the two important dynamical systems were studied,and we found that in certain conditions,there is a close relationship between the continuous mapping sequences {f_i} and the limit mapping f,also the dynamical systems(X,fog) and the dynamical systems(X,f),(X,g).The contents of the thesis are outlined as below:In chapter 1,we firstly reviewed the history of the uniformly convergent dynamical systems and composite dynamical systems,and then we introduced the importance of studying the two dynamical systems and gave a general framework for dynamical systems research.In chapter 2,we studied the relationship of dynamical behaviors between the continuous mapping sequences {f_i} and the limit mapping f,and gave a definition of strong uniform convergence.Under the condition that the continuous mapping sequences {f_i} strong uniformly converge to the mapping f,we proved that such property as topological minimality,topological transitivity,topological weak mixing,topological mixing can be embedded into the limit mapping f, and there is a inclusion relation on the Li-Yorke's chaos set(non-wandering set) between continuous mapping sequences {f_i} and the limit mapping f.In chapter 3,we discussed the relationship of dynamical behaviors between the dynamical systems(X,fog) and the dynamical systems(X,f),(X,g),and introduced a definition of absolutely expansive mapping and strong expansive mapping,and gave sufficient conditions under which(X,fog) has property as topological transitivity, topological mixing,topological strong transitivity,sensitive dependence on initial conditions.In Chapter 4,we summarize the results and innovation of this thesis,and present some views of perspectives for future study.