This paper is concerned with a class of finite-dimensional discrete spatiotemporal systems of the form {x1(m+1,n)=f1(x1(m,n−1),x1(m,n),x2(m,n),…,xk(m,n),x1(m,n+1))x2(m+1,n)=f2(x2(m,n−1),x1(m,n),x2(m,n),…,xk(m,n),x2(m,n+1))⋯⋯⋯⋯xk(m+1,n)=fk(xk(m,n−1),x1(m,n),x2(m,n),…,xk(m,n),xk(m,n+1)), where k>0 is an integer, fi:Rk+2→R is a real function for all i=1,2,…,k, m∈N0={0,1,2,…} and n∈Z={…,−1,0,1,…} (or,...