Seasonal Forcing in Rock-Paper-Scissors Population Dynamics

Abstract

We study a class of cyclic dominance models with seasonal forcing, extending the classical May-Leonard competition framework. By introducing time-periodic coefficients into the growth rates and the interaction terms, we explore how environmental seasonality influences the dynamics of three-species systems. Through analytical estimates and numerical simulations, we reveal the emergence of complex oscillatory behavior, including multi-year periodic cycles, transitions to heteroclinic cycles, and chaotic oscillations. Our results highlight how periodic modulation can destabilize stable periodic trajectories, generate novel attractors, and give rise to coexistence mechanisms not present in autonomous systems. These findings contribute to the understanding of biodiversity maintenance under realistic, temporally varying ecological conditions.