Nonequilibrium dynamics in a noise-induced predator-prey model

Understanding the dynamics of predator-prey systems in the presence of different environmental variability is crucial in ecology for forecasting population behaviour and ensuring ecosystem sustainability. It is a challenging aspect of studying spatio-temporal dynamics in the presence of environmental variability. We provide a noise-induced spatio-temporal predator-prey model to explore how temporal variability and spatial heterogeneity affect population dynamics. The multiplicative stochastic fluctuations in space and time are considered in the prey's growth rate and predator's death rate to capture the demographic noise in the ecosystem. We first examine the deterministic models by finding crucial parameters that influence the stability and dynamics of predator and prey populations, following their impact on spatio-temporal pattern formation. Using analytical tools and numerical simulations, we illuminate the mechanisms behind the observed dynamics and highlight the significance of demographic noise in generating ecological patterns. The numerical simulations show that the temporal variability introduced by noise leads to oscillations in population densities and alters the stability of the predator-prey system. Special attention is given to the spatio-temporal system when it fails to produce Turing patterns without noise, and the results show that linear demographic change can cause complex behaviours, such as self-organization, irregular oscillations, and nonequilibrium dynamics. Nevertheless, these findings broadly affect various ecological phenomena, including population persistence, species coexistence, long transients, and ecosystem resilience to demographic perturbations.