scholarly journals Almost Periodic Solution of a Modified Leslie-Gower Predator-Prey Model with Beddington-DeAngelis Functional Response

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zhimin Zhang
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Positive Almost Periodic Solution ◽  
Globally Attractive

We consider a predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov function, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Our results not only supplement but also improve some existing ones. One example is presented to verify our main results.

scholarly journals Almost Periodic Solution of a Modified Leslie-Gower Predator-Prey Model with Beddington-DeAngelis Functional Response and Feedback Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Kerong Zhang ◽  
Jianli Li ◽  
Aiwen Yu
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Globally Attractive

We consider a modified Leslie-Gower predator-prey model with the Beddington-DeAngelis functional response and feedback controls as follows:x˙t=xta1t-btxt-ctyt/αt+βtxt+γtyt-e1tut,u˙t=-d1tut+p1txt-τ,y˙t=yta2t-rtyt/xt+kt-e2tνt, andν˙(t)=-d2(t)ν(t)+p2(t)y(t-τ). Sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

Almost periodic solution of a modified Leslie–Gower predator–prey model with Holling-type II schemes and mutual interference

2014 ◽  
Vol 07 (03) ◽  
pp. 1450028 ◽  
Author(s):  
Shengbin Yu ◽  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Mutual Interference ◽  
Almost Periodic Solution ◽  
Type Ii ◽  
Almost Periodic ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Globally Attractive

In this paper, we consider a modified Leslie–Gower predator–prey model with Holling-type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov function, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Our results not only supplement but also improve some existing ones.

Permanence and almost periodic solution of a predator–prey discrete system with Holling IV functional response

2016 ◽  
Vol 09 (03) ◽  
pp. 1650035 ◽  
Author(s):  
Tiejun Zhou ◽  
Xiaolan Zhang ◽  
Meihong Xiang ◽  
Zhaohua Wu
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Time Model ◽  
Predator Prey ◽  
The Difference ◽  
Globally Attractive

A predator–prey discrete-time model with non-monotone functional response and density dependence is investigated in this paper. By using the comparison theorem of the difference equation, some sufficient conditions are obtained for the permanence of the system with variable coefficients. At the same time, a set of sufficient conditions about permanent of the system with almost periodic coefficients is also set up, which utilizes almost periodic characteristics of the system. Furthermore, the criteria which guarantee the existence of a globally attractive positive almost periodic solution of the system is established. An example is given to illustrate the feasibility of the obtained results.

scholarly journals Almost Periodic Solution of a Discrete Schoener’s Competition Model with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Hui Zhang ◽  
Yingqi Li ◽  
Bin Jing ◽  
Xiaofeng Fang ◽  
Jing Wang
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Competition Model ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
Globally Attractive

We consider an almost periodic discrete Schoener’s competition model with delays. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result.

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.

scholarly journals Almost Periodic Solution of a Diffusive Mixed System with Time Delay and Type III Functional Response

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Qiong Liu
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Mixed System ◽  
Uniform Persistence ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Razumikhin Technique ◽  
Predator Prey Model ◽  
Positive Almost Periodic Solution

A delayed predator-prey model with diffusion and competition is proposed. Some sufficient conditions on uniform persistence of the model have been obtained. By applying Liapunov-Razumikhin technique, we will point out, under almost periodic circumstances, a set of sufficient conditions that assure the existence and uniqueness of the positive almost periodic solution which is globally asymptotically stable.

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.

scholarly journals Permanence, Extinction, and Almost Periodic Solution of a Nicholson's Blowflies Model with Feedback Control and Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Haihui Wu ◽  
Shengbin Yu
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Feedback Control ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Nicholson’S Blowflies Model ◽  
Positive Almost Periodic Solution ◽  
Globally Attractive

A Nicholson's blowflies model with feedback control and time delay is studied. By applying the comparison theorem of the differential equation and fluctuation lemma and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence, extinction, and existence of a unique globally attractive positive almost periodic solution of the system are obtained. It is proved that the feedback control variable and time delay have no influence on the permanence and extinction of the system.

Dynamics of the Oscillative Solution for a Non-Linear Ecosystem with Impulsive Perturbation

2012 ◽  
Vol 226-228 ◽  
pp. 474-478
Author(s):  
Yuan Shun Tan ◽  
Hong Zhang
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Small Amplitude ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Pest Eradication ◽  
Globally Attractive ◽  
Ipm Strategy ◽  
Fixed Moment

In the present paper, we investigate an impulsive predator-prey model of integrated pest management(IPM) strategy. Other than the general Holling's functional response, an S-shaped mixed functional response is considered, simultaneously, we model this system assuming that the releasing of nature enemies and spraying of pesticides are impulsive at different fixed moment, which is more realistic comparing with at the same time. With the help of Floquet's theorem, small amplitude perturbation skills and comparison theorem involving multiple Liapunov functions, we show that under some sufficient conditions, the system exists an oscillative pest eradication periodic solution, which is local stable and globally attractive. Otherwise, the system is permanent. This result(threshold) provides us a very useful information for the control of ecosystem.

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