scholarly journals THE EXISTENCE OF PERIODIC SOLUTION OF A TWO-PATCHES PREDATOR-PREY DISPERSION DELAY MODELS WITH FUNCTIONAL RESPONSE

2003 ◽  
Vol 40 (5) ◽  
pp. 869-881 ◽  
Author(s):  
Zhengqiu Zhang ◽  
Zhicheng Wang
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Predator Prey ◽  
Delay Models

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 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.

DYNAMIC BEHAVIORS OF A KIND OF PREDATOR–PREY SYSTEM WITH IVLEV'S AND BEDDINGTON–DEANGELIS' FUNCTIONAL RESPONSE AND IMPULSIVE RELEASE

2008 ◽  
Vol 08 (04) ◽  
pp. 667-681
Author(s):  
HONGJIAN GUO ◽  
XINYU SONG ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Functional Response ◽  
Period Doubling ◽  
Continuous System ◽  
Impulsive System ◽  
Predator Prey ◽  
Impulsive Release ◽  
Predator System ◽  
Bifurcation Chaos

A kind of one-prey two-predator system with Ivlev's and Beddington–DeAngelis' functional response and impulsive release at fixed moments is presented. It is shown that the system has a prey-free periodic solution. By using the Floquet theory and small amplitude perturbation skills, it is proved that the prey-free periodic solution of the system is locally asymptotically stable when the period of impulsive release is less than a critical value. Furthermore, permanence of the system is investigated and the condition of permanence is obtained. Finally, numerical simulations show that the system has complex properties which include periodic solution, period-doubling bifurcation, chaos, chaotic windows, half-period bifurcation. A brief discussion on our results and their relation between the continuous system and the impulsive system are given. The results obtained in this paper are confirmed by numerical simulations.

scholarly journals On the dynamics of the impulsive predator-prey systems with Beddington – DeAngelis type functional response

2021 ◽  
Vol 73 (4) ◽  
pp. 523-543
Author(s):  
N. N. Pelen
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Analytic Structure ◽  
Predator Prey ◽  
Periodic Environment ◽  
Globally Attractive ◽  
Necessary And Sufficient

UDC 517.9 In this study, the two-dimensional predator-prey system with Beddington–DeAngelis type functional response with impulses is considered in a periodic environment. For this special case, necessary and sufficient conditions are found for the considered system when it has at least one -periodic solution. This result is mainly based on the continuation theorem in the coincidence degree theory and to get the globally attractive -periodic solution of the given system, an inequality is given as the necessary and sufficient condition by using the analytic structure of the system.  

scholarly journals Existence and Uniqueness of Globally Attractive Positive Almost Periodic Solution in a Predator-Prey Dynamic System with Beddington-DeAngelis Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wenquan Wu
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Time Scales ◽  
Fixed Point Theory ◽  
Continuous System ◽  
Point Theory ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Predator Prey ◽  
Positive Almost Periodic Solution

This paper is concerned with a predator-prey system with Beddington-DeAngelis functional response on time scales. By using the theory of exponential dichotomy on time scales and fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive (almost) periodic solution of the above system. Further, by means of Lyapunov functional, the global attractivity of the almost periodic solution for the above continuous system is also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples are given to illustrate the feasibility and effectiveness 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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