scholarly journals Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Weibing Wang ◽  
Jianhua Shen ◽  
Juan J. Nieto
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Effect ◽  
Two Dimensional ◽  
Stable Periodic Solution ◽  
Predator Prey ◽  
Prey System ◽  
Stable Periodic ◽  
Holling Type Functional Response

We considered a nonautonomous two dimensional predator-prey system with impulsive effect. Conditions for the permanence of the system and for the existence of a unique stable periodic solution are obtained.

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.

scholarly journals Behavior of the Solutions for Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on Periodic Time Scales in Shifts

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Neslihan Nesliye Pelen ◽  
Ayşe Feza Güvenilir ◽  
Billur Kaymakçalan
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Time Scales ◽  
Dynamic Systems ◽  
Two Dimensional ◽  
Predator Prey ◽  
Prey System ◽  
Special Case

We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system hasδ±-periodic solution.

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

scholarly journals Dynamic Behaviors of a Discrete Periodic Predator-Prey-Mutualist System

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Liya Yang ◽  
Xiangdong Xie ◽  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Cooperative Effect ◽  
Stable Periodic Solution ◽  
Predator Species ◽  
Predator Prey ◽  
Stable Periodic ◽  
Extinction Property ◽  
Globally Stable

A nonautonomous discrete predator-prey-mutualist system is proposed and studied in this paper. Sufficient conditions which ensure the permanence and existence of a unique globally stable periodic solution are obtained. We also investigate the extinction property of the predator species; our results indicate that if the cooperative effect between the prey and mutualist species is large enough, then the predator species will be driven to extinction due to the lack of enough food. Two examples together with numerical simulations show the feasibility of the main results.

EXISTENCE FOR PERIODIC SOLUTIONS OF A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME-VARYING DELAYS ON TIME SCALES

2010 ◽  
Vol 08 (03) ◽  
pp. 227-233
Author(s):  
HUIJUAN LI ◽  
ANPING LIU ◽  
ZUTAO HAO
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Functional Response ◽  
Time Scales ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Time Varying ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

In this paper, by using the continuation theorem of coincidence degree theory we study the existence of periodic solution for a two-species ratio-dependent predator-prey system with time-varying delays and Machaelis–Menten type functional response on time scales. Some new results are obtained.

scholarly journals Almost Periodic Sequence Solutions of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Zengji Du ◽  
Wenbin Li
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Periodic Sequence ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Predator Prey ◽  
Prey System

This paper considers a discrete predator-prey system with Beddington-DeAngelis functional response. Sufficient conditions are obtained for the existence of the almost periodic solution which is uniformly asymptotically stable by constructing a Lyapunov function.

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