A kind of non-traditional biomanipulation model with constant releasing fish

Abstract

On the basis of the ideas of non‐traditional biomanipulation control in fresh water body, a kind of nutrient–algae fish model is presented to investigate the effects of constant releasing fish on the nutrient and the algae. The threshold conditions for the extinction of the algae are obtained by discussing the stability of boundary equilibrium. The conditions for the coexistence of the algae and the fish are obtained by discussing the existence and stability of positive equilibrium. Besides, Hopf bifurcation is also analyzed by considering the parameter about the amount of the released fish. Furthermore, a kind of optimal problem is presented, and the necessary condition for the existence of the optimal solution is given by Pontryagin maximum principle. Finally, the mathematical results are verified by numerical simulations. The mathematical results show that there is a threshold amount of the released fish, above which the activity of releasing fish can control the growth of the algae and further reduce the probability of the algae bloom, but can not decrease the eutrophication level of the water body. Copyright © 2017 John Wiley & Sons, Ltd.

Bifurcation Based‐Delay Feedback Control Strategy for a Fractional‐Order Two‐Prey One‐Predator System

“…Many scholars have researched prey-predator systems with different harvest strategies [19,20,35]. However, when the density of predators is low, we may release predators to keep the balance of nature [36]. In the real world, the linear delayed feedback control tactic may have more practical means since we usually capture or release predators according to past date (the time scale is ).…”