Critical bait casting threshold of cage culture in open advective environments

Abstract

Cage culture, as a kind of aquaculture, is increasingly becoming the main way to provide aquatic products due to its merits of high output and easy management. However, the main issue for the fishermen to be concerned about is the determination of the reasonable amount of casting bait since excess feeding bait will not only deteriorate water quality but also increase farming costs while too little bait casting cannot meet the demand for capture. To this end, in this letter, we formulate a diffusive bait-fish model with advection term, aiming to determine the bait casting threshold that meets the demand for the breeding and causes less pollution to the water environment. We first prove the well-posedness of the proposed model. Then we define the net reproductive rate R0 determining the survival of the model and reveal the relationship between R0 and the bait casting rate. Besides, we show that the proposed model undergoes a forward supercritical transcritical bifurcation when the bait casting rate is equal to the critical value. Finally, we resort to a numerical example to support our theoretical results.