Attenuant cycles in periodically forced discrete-time age-structured population models

In discrete-time age-structured population models, a periodic environment is not always deleterious. We show that it is possible to have the average of the age class populations over an attracting cycle (in a periodic environment) not less than the average of the carrying capacities (in a corresponding constant environment). In our age-structured model, a periodic environment does not increase the average total biomass (no resonance). However, a periodic environment is disadvantageous for a population whenever there is no synchrony between the number of age classes and the period of the environment. As in periodically forced models without age-structure, we show that periodically forced age-structured population models support multiple attractors with complicated structures.