A pulse fishery model with closures as function of the catch: Conditions for sustainability

We present a model of single species fishery which alternates closed seasons with pulse captures. The novelty is that the length of a closed season is determined by the remaining stock size after the last capture. The process is described by a new type of impulsive differential equations recently introduced. The main result is a fishing effort threshold which determines either the sustainability of the fishery or the extinction of the resource.

► We propose a general deterministic fishery model.
► The model considers closed seasons alternated with impulsive captures.
► The non captured biomass determines the length of the next close season.
► The process is described by a new type of impulsive differential equation.
► We obtain a threshold on fishing effort ensuring sustainability.