Study Of Nonautonomous Cycle Point In Power System

The emergence of Chaos Theory has changed the publics’opinion of scientific determinism which had been hold for a long time. Uncertainty in determine dynamic systems has been studied in many fields of science since after the Butterfly effect was proposed in1970s.There are many definitions of uncertainty in topological dynamics, and they are not equivalence to each other. In this paper, some notions of chaos which have been defined in topological dynamics are introduced. Besides, the statuses of the arts and the relations among them are explored.Furthermore, as the rapid development of applied science, chaos in non-autonomous dynamical systems has been studied by many scholars. The definition of permutation dynamical systems of a periodic non-autonomous dynamical system is given and some conclusions are obtained in the relations between a periodic non-autonomous dynamical system and its permutation dynamical systems.We organized this paper as follows:In chapter1, as the introduction, we give a brief survey of the history of chaos.In chapter2, as the elementary of this paper, we introduce some notions of chaos in topological dynamics. Then after checking them separately, we explored the relations among them.In chapter3, we give our main results concerning dynamical properties of non-automatic dynamic systems. At first, we give the definition of the permutation dynamical systems of a periodic non-automatic dynamical system. And then, we prove that the trajectories of n-periodic points in a periodic non-autonomous dynamical dynamic system will remain unchanged in its specific permutation dynamical dynamics under some hypothesis, thus, the points are still n-periodic points of the permutation dynamical systems with the same trajectories.