On Non-autonomous Dynamical System Dependent Sensitive Research

The sensitivity which is also an characteristic of chaos, always plays an important role in dynamical system. In this paper, we mainly talk about the sensitivity and the relationship between sensitivity and other dynamical prop-erties in non-autonomous dynamical system and its hyperspace system. In non-autonomous dynamical system part, we give two kinds of definition of sensi-tivity at first. And then, we discuss the relationship of sensitivity between non-autonomous dynamical system and its any times iterative system. After that, we further study the relationship between sensitivity and other dynamical properties in non-autonomous dynamical system. Finally, the Banks theorem is generalized to the finitely generated non-autonomous dynamical system. In the hyperspace non-autonomous dynamical system part, we discuss the relationship of sensitivity between non-autonomous dynamical system and its hyperspace sys-tem. To a sensitive hyperspace non-autonomous dynamical system, we obtain a sufficient condition to ensure its any times iterative system is sensitive.