Stability and chaos in 2-D discrete systems

This paper is concerned with 2-D discrete systems of the formxm+1,n=f(xm,n,xm,n+1),where f : R2 → R is a function, m, n ∈ N0 = {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.