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.

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.

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 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.

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.

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.

scholarly journals Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

Dynamical behaviors of a diffusive predator–prey model with Beddington–DeAngelis functional response and disease in the prey

2017 ◽  
Vol 10 (08) ◽  
pp. 1750119 ◽  
Author(s):  
Wensheng Yang
Keyword(s):  
Lyapunov Function ◽  
Iterative Method ◽  
Functional Response ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey Model

The dynamical behaviors of a diffusive predator–prey model with Beddington–DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones.

scholarly journals Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Parameter Configuration ◽  
Sufficient And Necessary Conditions ◽  
Steady State Solutions

We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration.

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