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 Existence of Unique and Global Asymptotically Stable Almost Periodic Solution of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response and Density Dependent

2018 ◽  
Vol 52 (1) ◽  
pp. 87-105
Author(s):  
Cosme Duque
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Predator Prey ◽  
Density Dependent ◽  
Prey System ◽  
El Sistema

El objetivo principal de este artículo es el de estudiar la dinámica de un sistema depredador-presa discreto con respuesta funcional Beddington-DeAngelis y densamente dependiente del depredador, asumiendo que los coeficientes involucrados en el sistema son casi periódicos. De forma más concreta, bajo ciertas condiciones, probaremos la existencia de una única solución casi periódica la cual es globalmente atractiva. Exhibimos algunos ejemplos numéricos de los resultados.

scholarly journals Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hui Zhang ◽  
Feng Feng ◽  
Bin Jing ◽  
Yingqi Li
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Positive Almost Periodic Solution ◽  
Mutualism System

We consider an almost periodic multispecies discrete Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. An example together with numerical simulation indicates the feasibility of the main result.

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.

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 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 Dynamics of a nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses

2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Periodic Case ◽  
Almost Periodic ◽  
Functional Responses ◽  
Predator Prey ◽  
Prey System ◽  
Nonautonomous Case

A nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses is investigated. For general nonautonomous case, positive invariance, permanence, and globally asymptotic stability for the system are studied. For the periodic (almost periodic) case, sufficient conditions for existence, uniqueness, and stability of a positive periodic (almost periodic) solution are obtained.

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.

Dynamics of a non-autonomous ratio-dependent predator—prey system

2003 ◽  
Vol 133 (1) ◽  
pp. 97-118 ◽  
Author(s):  
Meng Fan ◽  
Qian Wang ◽  
Xingfu Zou
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Positive Periodic Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Predator Prey ◽  
Prey System ◽  
Autonomous Case ◽  
Positive Almost Periodic Solution ◽  
Ratio Dependent

We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

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.

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