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    This work discusses the effects of periodic forcing on attracting cycles and more complicated attractors for autonomous systems of nonlinear difference equations. Results indicate that an attractor for a periodically forced dynamical system may inherit structure from an attractor of the autonomous (unforced) system and also from the periodicity of the forcing. In particular, a method is presented which shows that if the amplitude of the k-periodic forcing is small enough, then the attractor for the forced system is the union of k homeomorphic subsets. Examples from population biology and genetics indicate that each subset is also homeomorphic to the attractor of the original autonomous dynamical system.

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    Selgrade, James F.; Roberds, James H. 2001. On the structure of attractors for discrete, periodically forced systems with applications to population models. Physica D. 158: 69-82

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