Study On The Dynamical Behaviors Of Two Types Of Hybrid Cellular Automata

In this thesis,the dynamical behaviors of two types of hybrid cellular automata are researched from the viewpoint of symbolic dynamic.First of all,study on HTCA(3,13,10),it exhibits a wide range of traveling and stationary localisations and generates a lot of gliders in hybrid mechanism.Using quantitative approach,we get down to search an exhaustive gliders from the HTCA(3,13,10)and classify them.After classifying and coding of the newly discovered gliders,we analyze the chaotic dynamics properties of the glider in symbolic dynamics viewpoint.Specially,it is proved that the glider can be expressed as a particular subsystem with complicated dynamical properties,which possess topologically mixing and positive topological entropy.So that it have chaotic in the sense of both Li-Yorke and Devaney in corresponding subsystems.Secondly,the dynamics properties of hybrid cellular automata(HCA)rule 30 and 60 are investigated in the method of computational simulation with the periodic boundary condition and symbolic dynamic system in the bi-infinite symbolic sequence space.The local evolution rules of HCA(30,60),composed by elementary cellular automata rule 30 and rule 60,is specified to execute Rule 30 at odd site of the cell array(Rule 60 at even site of the cell array).HCA(30,60),exhibited the shift dynamic behavior in space-time pattern.HCA(30,60)is topologically mixing on its global attractor and possesses the positive topological entropy.Therefore,HCA(30,60)is chaotic in the sense of both LiYorke and Devaney.This thesis is organized as follows: The first chapter introduces the background and development situation of cellular automata,and the basic concept of cellular automata.The second chapter is preliminary knowledge,it introduces the basic concepts of symbol dynamical system,and introduces the glider simply.The third chapter explores the basic concepts of HTCA(3,13,10),discusses its space-time patterns.Chapter four explores several computational simulation results of HCA(30,60)on a special subset of the biinfinite sequence space and identifies the global attractor of HCA(30,60)which is simply a subshift of finite type and demonstrates the chaotic dynamics of HCA(30,60),that is,HCA(30,60)is topologically mixing on the global attractor and possesses the positive topological entropy.At last,the fifth chapter highlights the main results and prospects for future studies.