scholarly journals Effects of prey refuge on a ratio-dependent predator–prey model with stage-structure of prey population

2013 ◽  
Vol 37 (6) ◽  
pp. 4337-4349 ◽  
Author(s):  
Sapna Devi
Keyword(s):  
Stage Structure ◽  
Prey Population ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

scholarly journals Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Lingshu Wang ◽  
Guanghui Feng
Keyword(s):  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Comparison Arguments ◽  
Ratio Dependent ◽  
Iteration Technique ◽  
Coexistence Equilibrium

A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, whenτ=τ0. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.

RATIO-DEPENDENT PREDATOR–PREY MODEL WITH STAGE STRUCTURE AND TIME DELAY

2012 ◽  
Vol 05 (04) ◽  
pp. 1250014 ◽  
Author(s):  
LIJUAN ZHA ◽  
JING-AN CUI ◽  
XUEYONG ZHOU
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Predator Prey Models

Ratio-dependent predator–prey models are favored by many animal ecologists recently as more suitable ones for predator–prey interactions where predation involves searching process. In this paper, a ratio-dependent predator–prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.

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

2016 ◽  
Vol 09 (04) ◽  
pp. 1650058 ◽  
Author(s):  
Fengying Wei ◽  
Qiuyue Fu
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Characteristic Functions ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Globally Asymptotic Stability ◽  
Predator Prey Model ◽  
Prey Model

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.

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