Research On Several Chaoticities Of Non-autonomous Dynamical System In Hyperspace

The non-autonomous dynamical system,autonomous dynamical system and their corresponding hyperspace dynamical system having been the hot topic of many scholars,the research on the non-autonomous dynamic system in hyperspace has become a rel-atively new issue.Here,we' 11 study several chaotic properties of Li-Yorke sensitivity,distribution of chaos,F-sensitivity and multiple sensitivity on non-autonomous dynamical systems in hyperspace.Firstly,Li-Yorke sensitivity and distributed chaos of the iterative system of non-autonomous dynamical system(X,f_1??^[k])are introduced into hyperspace.Li-Yorke sen-sitivity and distribution chaos of the iterative system of hyperspace non-autonomous dynamical system(K?X?f_1??^[k])are discussed.We'll also study the condition that holds of Li-Yorke sensitivity and P1-chaos of the system(K?X?,f_1,?)under its iteration.In addition,Li-Yorke sensitivity implication relationship between the iterative system of two hyperspace non-autonomous dynamical systems and its complex product dynamic system is analyzed.Secondly,by means of the introduction of hyperspace system's F-sensitivity and multiple sensitivity into a more general non-autonomous dynamical system,the F-sensitivity and multiple sensitivity of hyperspace non-autonomous dynamical system?K?X?,f1,??are discussed,which is divided into two parts:Part one discusses the F-sensitive and multiple sensitive implicative relationship between the non-autonomous dy-namical system and its corresponding hyperspace non-autonomous dynamical system.In part two,we discuss the implicit relationship of F-sensitive between two non-autonomous dynamical systems and the composite product dynamical system of their corresponding hyperspace non-autonomous dynamical systems.Besides,we also discusses the IF-sensitive and multiple sensitive implicative relationship between two hyperspace non-autonomous dynamical systems and their complex product dynamical systems.In this paper,the idea of several kinds of chaotic properties of hyperspace non-autonomous dynamical systems can be applied to the study of the chaotic properties of other hyperspace non-autonomous dynamical systems.