Chaos in the sense of Li–Yorke in coupled map lattices

Abstract

This paper is mainly concerned with coupled map lattice (CML) of the form x m + 1 , n = ( 1 - ε ) f ( x m , n ) + 0.5 ε { f ( x m , n - 1 ) + f ( x m , n + 1 ) } , where f : R → R is a function and m ∈ N 0 = { 0 , 1 , … } and n ∈ Z = { … ,- 1 , 0 , 1 , … } . A new definition of chaos in discrete spatiotemporal systems in the sense of Li–Yorke is given and one sufficient condition for this system to be chaotic in the sense of Li–Yorke is derived.