Experiments in predator–prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects. However, simulating stochastic individual based models can be extremely demanding, especially when the sample size is large. Hence, we propose an alternative simulation approach, whose computation cost is lower than the one of the classic stochastic algorithms. First, we describe the agent-based model with predator–prey dynamics, and its mean-field approximation. Then, we provide a consistency result for the novel stochastic algorithm at the microscopic and mesoscopic scale. Finally, we perform different numerical experiments in order to test the efficiency of the proposed algorithm, focusing also on the analysis of the different nature of oscillations between mean-field and stochastic simulations.
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