Stability of Periodic Solutions of Nonlinear Integrodifferential Systems

Abstract

We apply the two-timing perturbation procedure to problems of bifurcation of periodic solutions of nonlinear integrodifferential equations of a type arising in population dynamics. This yields also the stability of the bifurcating branch. Next a Floquet theory for linear integrodifferential equations with periodic coefficients is stated along with three theorems characterizing the stability of periodic solutions of nonlinear equations of the kind referred to above. This theory is shown to confirm the stability results of the perturbation procedure.