A singular stochastic control model for sustainable population management of the fish-eating waterfowl Phalacrocorax carbo

A simplified stochastic optimization model for logistic dynamics with control-dependent carrying capacity

“…It is shown that the HJB equation has a unique viscosity solution: an appropriate weak solution for this kind of equations [16]. The HJB equation is not exactly-solvable as in those arising in other ecological problems [59,60], but asymptotic estimates of its solution are found. A finite difference scheme for approximation of the solution is then presented.…”

“…With a performance index to be minimized or maximized, owing to the dynamic programming principle, finding the optimal control reduces to solving a Hamilton-Jacobi-Bellman (HJB) equation: a degenerate elliptic or parabolic equation whose functional form is problem-dependent [21]. Both mathematical and numerical approaches have been addressed for analysis of HJB equations in many problems, ranging from financial [17], economic [1], and insurance problems [14] to biological [62], environmental [12], and ecological problems [60]. Neilan et al [40] reviewed recent progresses of numerical schemes for solving HJB and related nonlinear differential equations.…”

An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management

“…Finally, the system (52) is discretized with the conventional forward Euler method. The parameters are set as μ = 1.7× 10 -1 (1/year), σ = 5.3× 10 -1 (1/year 1/2 ), m = 1.8 (-), M = 0.5 (-), δ = 1.0 (1/year), r = 5.0 × 10 -4 (-), R = 1.0 × 10 -1 (-), k 0 = 1.0 × 10 1 (-) and k 1 = 1.0 × 10 0 (-) [2]. These parameters satisfy the assumptions (20) through (22).…”

“…1 Graduate School of Agriculture, Kyoto University, Kyoto City, Japan. 2 Research Fellow of Japan Society for the Promotion of Science, Tokyo, Japan. 3 Graduate School of Natural Science and Technology, Shimane University, Matsue City, Japan.…”

“…Management of animal population, such as fishery resources and their predators, is an important ecological problem. Such examples include aquaculture of Plecoglossus altivelis (P. altivelis, Ayu) in Japan [1], extermination of its predator bird Phalacrocorax carbo (P. carbo, Great cormorant) [2,3], agricultural crops damage by a wild boar Sus scrofa in Europe [4], and feeding damage from many insects to soybean seeds [5]. Recently, fisheating bird P. carbo population has been increasing worldwide, such as in Japan [6], Europe [7], North America [8], and Greenland [9].…”