About the singularities and bifurcations of double indices recursion sequences

Abstract

This paper reports analytical and numerical investigations about the singularities and bifurcations of a new class of discrete dynamical systems defined generally by the following 2-D discrete systems: y m+1,n+1 = f (y m,n , y m+1,n , y m,n+1 ); we consider particularly the case y m+1,n+1 = f (y m,n , y m+1,n ).First, we give the analytical solution in the linear case, as it was introduced by Lagrange. Second, we propose some definitions for the singularities and bifurcations of non-linear systems with double indices and we illustrate these with numerical examples.