||Analysis of a predator-prey model with a seasonally forced prey growth rate
Many natural systems are subject to seasonal environmental change. As a consequence many species exhibit seasonal changes in their life history parameters - such as a peak in the birth rate in spring. There have been two main ways in which systems with seasonal forcing have been studied: a bifurcation approach and a simulation-based resonance diagram. We combine these two methods in order to gain a comprehensive view of the potential solution behaviours for a predator-prey system with a seasonally forced prey growth rate. We consider separately how forcing influences the system when the unforced dynamics have monotonic decay to the coexistence steady state, oscillatory decay, or stable limit cycles. The range of behaviour the system can respond with includes quasi-periodicity and multi-year cycles, and there are parameter ranges with co-existing multi-year cycles of the same or different period. We show that the level of oscillation in the unforced system has a large effect on the range of behaviour when the system is seasonally forced.