  This paper presents a system of stochastic differential equations (SDEs) as
mathematical model to describe the spatial-temporal dynamics of predator-prey
system in an artificial aquatic environment with schooling behavior imposed
upon the associated prey. The proposed model follows the particle-like approach
where interactions among the associated units are manifested through
combination of attractive and repulsive forces analogous to the ones occurred
in molecular physics. Two hunting tactics of the predator are proposed and
integrated into the general model, namely the center-attacking and the
nearest-attacking strategy. Emphasis is placed upon demonstrating the capacity
of the proposed model in: (i) discovering the predator-avoidance patterns of
the schooling prey, and (ii) showing the benefit of constituting large prey
school in better escaping the predator's attack. Based on numerical simulations
upon the proposed model, four predator-avoidance patterns of the schooling prey
are discovered, namely Split and Reunion, Split and Separate into Two Groups,
Scattered, and Maintain Formation and Distance. The proposed model also
successfully demonstrates the benefit of constituting large group of schooling
prey in mitigating predation risk. Such findings are in agreement with
real-life observations of the natural aquatic ecosystem, hence confirming the
validity and exactitude of the proposed model.
