Abstract

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).