Lotka-Volterra predator-prey lattice model with a time-dependent carrying capacity.

Environmental variability is crucial to understanding species coexistence. Traditional population dynamics models seldom consider coupling environmental variability to the intrinsic noise of the ecological system. This study aims to investigate the effect of environmental change on the behavior of the two-species Lotka-Volterra lattice model for predator-prey competition and coexistence. It is well-established that a predator extinction phase transition occurs in lattice models with on-site restriction (i.e., finite carrying capacity), and it is absent when the carrying capacity is infinite. We model an environment with a varying nutrient abundance through a temporally changing carrying capacity, which is here implemented as a square-wave signal with a constant frequency. The output of the stochastic Monte Carlo simulation is used to study the density oscillations in this periodically driven system and investigate resonance phenomena. Additionally, we compute temporal correlations and study the effect of changing the carrying capacity on the predator extinction phase transition. Preliminary results show a period-doubling effect for specific predation rates, where the density oscillation frequency is twice the carrying capacity frequency.