Existence and stability of nontrivial periodic solutions of periodically forced discrete dynamical Systems

The local existence and local asymptotic stability of nontrivial p-periodic solutions of p-periodically forced discrete systems are proven using Liapunov-Schmidt methods. The periodic solutions bifurcate transcritically from the trivial solution at the critical value n=ncr of the bifurcation parameter with a typical exchange of stability. If the trivial solution loses (gains) stability as n is increased through ncr , then the periodic solutions on the nontrivial bifurcating branch are locally asymptotically stable if and only if they correspond to n>ncr (n ncr ).