scholarly journals Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Wahiba Khellaf ◽  
Nasreddine Hamri
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Qualitative Behavior ◽  
Uniform Persistence ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Prey System ◽  
Predator Prey Models ◽  
Type Ii Functional Response

We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.

scholarly journals Dynamic Behaviors of a Nonautonomous Discrete Predator-Prey System Incorporating a Prey Refuge and Holling Type II Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Wanlin Chen ◽  
Yuhua Lin
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Type Ii Functional Response

A nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response is studied in this paper. A set of sufficient conditions which guarantee the persistence and global stability of the system are obtained, respectively. Our results show that if refuge is large enough then predator species will be driven to extinction due to the lack of enough food. Two examples together with their numerical simulations show the feasibility of the main results.

DYNAMIC COMPLEXITIES OF HOLLING TYPE II FUNCTIONAL RESPONSE PREDATOR–PREY SYSTEM WITH DIGEST DELAY AND IMPULSIVE HARVESTING ON THE PREY

2009 ◽  
Vol 02 (02) ◽  
pp. 229-242 ◽  
Author(s):  
JIANWEN JIA ◽  
HUI CAO
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Impulsive Differential Equation ◽  
Global Attractivity ◽  
Sufficient Condition ◽  
Type Ii ◽  
Predator Prey ◽  
Prey System ◽  
Impulsive Harvesting ◽  
Type Ii Functional Response

In this paper, we introduce and study Holling type II functional response predator–prey system with digest delay and impulsive harvesting on the prey, which contains with periodically pulsed on the prey and time delay on the predator. We investigate the existence and global attractivity of the predator-extinction periodic solutions of the system. By using the theory on delay functional and impulsive differential equation, we obtain the sufficient condition with time delay and impulsive perturbations for the permanence of the system.

scholarly journals Average Conditions for the Permanence of a Bounded Discrete Predator-Prey System

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Functional Response ◽  
Lower Bounds ◽  
Population Models ◽  
Upper And Lower Bounds ◽  
Multiple Delays ◽  
Type Ii ◽  
Predator Prey ◽  
Prey System ◽  
Bounded System ◽  
Type Ii Functional Response

Average conditions are obtained for the permanence of a discrete bounded system with Holling type II functional responseu(n+1)=u(n)exp{a(n)-b(n)u(n)-c(n)v(n)/(u(n)+m(n)v(n))},v(n+1)=v(n)exp{-d(n)+e(n)u(n)/(u(n)+m(n)v(n))}.The method involves the application of estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.

Global Stability of a Non-Smooth Predator–Prey System with Holling I Functional Response and Refuge Effect

2014 ◽  
Vol 595 ◽  
pp. 283-288 ◽  
Author(s):  
Yuan Tian ◽  
Hai Ting Sun ◽  
Yu Xia He
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Tangent Point ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Refuge Effect ◽  
Prey System ◽  
Trivial Equilibrium ◽  
The Stability ◽  
Regular Equilibrium

This paper analyses the dynamics of a non-smooth predator-prey model with refuge effect, where the functional response is taken as Holling I type. To begin with, some preliminaries and the existence of regular, virtual, pseudo-equilibrium and tangent point are established. Then, the stability of trivial equilibrium and predator free equilibrium is discussed. Furthermore, it is shown that the regular equilibrium and the pseudo-equilibrium cannot coexist. Finally, the conclusion is given.

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