Stability and chaos in 2-D discrete systems

This paper is concerned with 2-D discrete systems of the form x m + 1 , n = f ( x m , n , x m , n + 1 ) , where f : R 2 → R is a function, m, n ∈ N 0 ={0,1,2,…}. Some sufficient conditions for this system to be stable and a verification of this system to be chaotic in the sense of Devaney, respectively, are derived.