Numerical simulation of a Hamilton-Jacobi-Bellman equation for optimal management strategy of released Plecoglossus altivelis in river systems

Abstract

A stochastic differential equation model for population dynamics of released Plecoglossus altivelis (Ayu) in a river system subject to feeding damage by Phalacrocorax carbo (Great Cormorant) and fishing activity by human is proposed. A stochastic optimal control problem to maximize the sum of the cost of countermeasure to prevent the feeding damage and the benefit of harvesting the fish is formulated, which ultimately reduces to solving a Hamilton-Jacobi-Bellman equation. Application of a Petrov-Galerkin finite element scheme to the equation successfully computes the optimal management strategies for the population dynamics of P. altivelis in a real river system and ecological and economical indices to verify them.