A stochastic differential equation model for predator-avoidance fish schooling

This paper presents a mathematical model based on stochastic differential equations (SDEs) to depict the dynamics of a predator–prey system in an aquatic environment characterized by schooling behavior among the prey. The model employs a particle-like approach, incorporating attractive and repulsive forces, akin to phenomena observed in molecular physics, to capture the interactions among the constituent units. Two hunting tactics of the predator, center-attacking and nearest-attacking strategies, are integrated into the model. Numerical simulations of this model unveil four distinct predator-avoidance patterns exhibited by schooling prey: Split and Reunion, Split and Separate into Two Groups, Scattered, and Maintain Formation and Distance. Our results also confirm the effectiveness of large groups of schooling prey in mitigating predation risk, consistent with real-life observations in natural aquatic ecosystems. These findings validate the accuracy and applicability of our model.