caa a22 4500 445361859 CHVBK 20180317142917.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11071-011-9952-2 doi (NATIONALLICENCE)springer-10.1007/s11071-011-9952-2 About the singularities and bifurcations of double indices recursion sequences [Elektronische Daten] [L. Randriamihamison, A. Taha] 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. Springer Science+Business Media B.V., 2011 Fixed point nationallicence Singularity nationallicence Bifurcation nationallicence Double indices sequence nationallicence Randriamihamison L. IPST-Cnam, 39 alles Jules Guesde, BP 61517, 31015, Toulouse cedex 6, France aut Taha A. LATTIS, INSAT, 135 avenue de Rangueil, 31077, Toulouse cedex 4, France aut Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 795-808 0924-090X 66:4<795 2011 66 11071 https://doi.org/10.1007/s11071-011-9952-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-011-9952-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Randriamihamison L. IPST-Cnam, 39 alles Jules Guesde, BP 61517, 31015, Toulouse cedex 6, France aut NATIONALLICENCE 700 1- Taha A. LATTIS, INSAT, 135 avenue de Rangueil, 31077, Toulouse cedex 4, France aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 795-808 0924-090X 66:4<795 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer