An impulsive fishery model with environmental stochasticity. Feasibility.
An environmental random-effect over a deterministic population model of a resource (e.g., a fish stock) is introduced. It is assumed that the harvest activity is concentrated at a non-predetermined sequence of instants, at which the abundance reaches a certain predetermined level, then falls abruptly by a constant capture quota (pulse harvesting). So, the abundance is modeled by a stochastic impulsive type differential equation, incorporating a standard Brownian motion in the per capita rate of growth. With this random effect, the pulse times are "stopping times" of the stochastic process. The proof of the finite expectation of the next access time, i.e., the feasibility of regulation, is the main result.
Universidad Tecnológica Metropolitana, Dieciocho 161, Santiago, Chile.
Ricardo
R
Castro-Santis
Facultad de Ciencias Básicas, Universidad Católica del Maule, Avda. San Miguel 3605 Talca, Chile. Electronic address: fcordova@ucm.cl.
Fernando
F
Córdova-Lepe
Departamento de Matemática, Universidad del Bío-Bío, Avda. Collao Concepción 1202, Chile.
Walter
W
Chambio
D000818:Animals; D004777:Environment; D005398:Fisheries; D005399:Fishes; D008962:Models, Theoretical; D013269:Stochastic Processes
Environmental stochasticity; Feasibility; Fishery model; Pulse harvesting