The effect of harvesting on a predator–prey system with stage structure

Globally asymptotic stability of a predator–prey model with stage structure incorporating prey refuge

This paper focuses on the stabilities of the equilibria to a predator–prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.

A time delay predator-prey system with three-stage-structure

A predator-prey system was studied that has a discrete delay, stage-structure, and Beddington-DeAngelis functional response, where predator species has three stages, immature, mature, and old age stages. By using of Mawhin's continuous theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution.

DYNAMIC BEHAVIOR ANALYSIS OF A DIFFERENTIAL-ALGEBRAIC PREDATOR–PREY SYSTEM WITH PREY HARVESTING

This paper studies a differential-algebraic predator–prey system with prey harvesting, which consists of two differential equations and an algebraic equation. By using the differential-algebraic system theory, bifurcation theory and formal series expansions, we investigate the Hopf bifurcation and center stability of the differential-algebraic predator–prey system. Some sufficient conditions on these issues are obtained. In addition, numerical simulations illustrate the effectiveness of our results and their biological implications are discussed.

GLOBAL ANALYSIS OF A HARVESTED PREDATOR–PREY MODEL INCORPORATING A CONSTANT PREY REFUGE

A predator–prey model with Holling type II functional response incorporating a constant prey refuge and independent harvesting in either species is investigated. Some sufficient conditions of the instability and stability properties to the equilibria and the existence and uniqueness to limit cycles for the model are obtained. We also show that influence of prey refuge and harvesting efforts on equilibrium density values. One of the surprising finding is that for fixed prey refuge, harvesting has no influence on the final density of the prey species, while the density of predator species is decreasing with the increasing of harvesting effort on prey species and the fixation of harvesting effort on predator species. Numerical simulations are carried out to illustrate the obtained results and the dependence of the dynamic behavior on the harvesting efforts or prey refuge.