N-adic Set And Distributional Chaos In Coupled Map Lattices

This paper introduces the history of chaos phenomenon and the definitions of some importantchaos. Later this paper is mainly concerned with coupled map lattice(CML) of the formxm+1, n=(1-ε) f (xm, n)0.5ε{f (xm, n-1) f (xm, n+1)}where f:R Ris a continuousfunction andm N0{0,1…}and n {…1,0,1}. Distributional chaos in discretespatiotemporal systems is given one sufficient condition for this system to be distributionalchaotic. This paper also gives a sufficient condition for this system having an uncountabledistributively chaotic set on different metric spaces. And also gives a sufficient condition forthis system having an uncountable distributively chaotic set on different metric spaces when ithas n-adic set. This paper briefly introduces the relationship between each point in the chaoticset and chain recurrent points, too. And by means of entropy, we proves that n-adic systems inwhich n is not a power of2are Devaney chaotic, Wiggins chaotic, distributional chaos in asequence, distributional chaos, Martelli’s chaotic, W-chaotic， Block and copple chaotic.