Cyclic predator-prey models with time varying rates

Cyclic predator-prey models have been shown to establish stable spiral waves that allow for long term species coexistence. In this study, we analyze a system in which we change the characteristics of species interactions over time, namely their predation and reproduction rates, using the May-Leonard model in order to replicate seasons and other environmental factors that occur in real life ecologies. We compare the effects of changing the reproduction rates vs the predation rates and find a change in the reproduction rates creates a much stronger effect on species densities and spiral size. We vary both rates periodically by using square and sinusoidal waves, and randomly such that at every time step, there is a set probability for the rates to change between two values. Discrete Fourier analysis of the auto-correlation function is done to find the characteristic frequencies and hence the spiral size of the system during different regimes. Numerical analysis of the average density is also done in the different regimes to provide more data. We extend our analysis to other multiple species games as well.