scholarly journals Permanence for a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jiangbin Chen ◽  
Shengbin Yu
Keyword(s):  
Feedback Control ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Control Variables ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A new set of sufficient conditions for the permanence of a ratio-dependent predator-prey system with Holling type III functional response and feedback controls are obtained. The result shows that feedback control variables have no influence on the persistent property of the system, thus improving and supplementing the main result of Yang (2008).

scholarly journals Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Jinghui Yang
Keyword(s):  
Lyapunov Function ◽  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Species ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator speciesywill be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.

The Permanence of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

2013 ◽  
Vol 765-767 ◽  
pp. 327-330
Author(s):  
Chang You Wang ◽  
Xiang Wei Li ◽  
Hong Yuan
Keyword(s):  
Feedback Control ◽  
Sufficient Conditions ◽  
Functional Responses ◽  
Feedback Controls ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Analysis Technique ◽  
Ratio Dependent

This paper is concerned with a Lotka-Volterra predator-prey system with ratio-dependent functional responses and feedback controls. By developing a new analysis technique, we establish the sufficient conditions which guarantee the permanence of the model.

scholarly journals Periodic solutions and stability for a delayed discrete ratio-dependent predator-prey system with Holling-type functional response

2004 ◽  
Vol 2004 (2) ◽  
pp. 325-343 ◽  
Author(s):  
Lin-Lin Wang ◽  
Wan-Tong Li
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Globally Asymptotical Stability ◽  
Ratio Dependent

The existence of positive periodic solutions for a delayed discrete predator-prey model with Holling-type-III functional responseN1(k+1)=N1(k)exp{b1(k)−a1(k)N1(k−[τ1])−α1(k)N1(k)N2(k)/(N12(k)+m2N22(k))},N2(k+1)=N2(k)exp{−b2(k)+α2(k)N12(k−[τ2])/(N12(k−[τ2])+m2N22(k−[τ2]))}is established by using the coincidence degree theory. We also present sufficient conditions for the globally asymptotical stability of this system when all the delays are zero. Our investigation gives an affirmative exemplum for the claim that the ratio-dependent predator-prey theory is more reasonable than the traditional prey-dependent predator-prey theory.

scholarly journals Dynamical behavior of a stochastic ratio-dependent predator-prey system with Holling type IV functional response

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6549-6562
Author(s):  
Jing Fu ◽  
Daqing Jiang ◽  
Ningzhong Shi ◽  
Tasawar Hayat ◽  
Baslur Abmad
Keyword(s):  
Functional Response ◽  
Stochastic Equation ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Dynamical Properties ◽  
Ratio Dependent

In this paper, we investigate the dynamical properties of a stochastic ratio-dependent predatorprey system with Holling type IV functional response. The existence of the globally positive solutions to the system with positive initial value is shown employing comparison theorem of stochastic equation and It??s formula. We derived some sufficient conditions for the persistence in mean and extinction. This system has a stable stationary distribution which is ergodic. Numerical simulations are carried out for further support of present research.

scholarly journals Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
Xuepeng Li ◽  
Wensheng Yang
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Negative Feedback ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Prey Population ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent ◽  
Nonmonotonic Functional Response

Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay    are obtained, where and stand for the density of the prey and the predator, respectively, and is a constant. stands for the time delays due to negative feedback of the prey population.

scholarly journals Permanence and Global Attractivity of a Delayed Discrete Predator-Prey System with General Holling-Type Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Lijuan Chen ◽  
Junyan Xu ◽  
Zhong Li
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Prey ◽  
Prey System ◽  
Holling Type Functional Response

This paper discusses a delayed discrete predator-prey system with general Holling-type functional response and feedback controls. Firstly, sufficient conditions are obtained for the permanence of the system. After that, under some additional conditions, we show that the periodic solution of the system is global stable.

On a delay ratio-dependent predator–prey system with feedback controls and shelter for the prey

2018 ◽  
Vol 11 (07) ◽  
pp. 1850095
Author(s):  
Changyou Wang ◽  
Linrui Li ◽  
Yuqian Zhou ◽  
Rui Li
Keyword(s):  
Numerical Solutions ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Feedback Controls ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Ratio Dependent ◽  
Predator Prey Models

In this paper, a class of three-species multi-delay Lotka–Volterra ratio-dependent predator–prey model with feedback controls and shelter for the prey is considered. A set of easily verifiable sufficient conditions which guarantees the permanence of the system and the global attractivity of positive solution for the predator–prey system are established by developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function. Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In addition, some numerical solutions of the equations describing the system are given to show that the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator–prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system. At the same time, the influence of the delays and shelters on the dynamics behavior of the system is also considered by solving numerically the predator–prey models.

BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT

2021 ◽  
pp. 1-28
Author(s):  
ANURAJ SINGH ◽  
PREETI DEOLIA
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Flip Bifurcation ◽  
Bifurcation Structure ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Wide Range

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

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