scholarly journals Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Zhang ◽  
Bin Jing ◽  
Yingqi Li ◽  
Xiaofeng Fang
Keyword(s):  
Periodic Solution ◽  
Global Analysis ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences ◽  
Globally Attractive ◽  
Mutualism System

This paper discusses a discrete multispecies Lotka-Volterra mutualism system. We first obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.

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 Solutions of a Discrete Mutualism Model with Feedback Controls

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Zheng Wang ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Existence And Uniqueness ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Periodic Sequences ◽  
Mutualism Model ◽  
Almost Periodic Sequences

We consider a discrete mutualism model with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.

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.

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.

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 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.

THE STABILITY AND ALMOST PERIODIC SOLUTION FOR GENERALIZED LOGISTIC ALMOST PERIODIC SYSTEM WITH DELAYS

2011 ◽  
Vol 04 (03) ◽  
pp. 313-328 ◽  
Author(s):  
XIANGLAI ZHUO
Keyword(s):  
Periodic Solution ◽  
Periodic System ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Computational Techniques ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Discrete Delays ◽  
The Stability

The stability and almost periodic solution for generalized logistic almost periodic system with infinite and discrete delays is considered. Some sufficient conditions for the boundedness of the system are obtained to guarantee that the system is globally asymptotically stable. We also show that the almost periodic system has a unique globally asymptotically stable strictly positive almost periodic solution by using the almost periodic functional Hull theory and new computational techniques. Furthermore, some recent results are improved, and an open question is answered.

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 Stability Analysis of Three-Species Almost Periodic Competition Models with Grazing Rates and Diffusions

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Chang-you Wang ◽  
Rui-fang Wang ◽  
Ming Yi ◽  
Rui Li
Keyword(s):  
Periodic Solution ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Almost Periodic Solution ◽  
Species Competition ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Positive Space

Almost periodic solution of a three-species competition system with grazing rates and diffusions is investigated. By using the method of upper and lower solutions and Schauder fixed point theorem as well as Lyapunov stability theory, we give sufficient conditions to ensure the existence and globally asymptotically stable for the strictly positive space homogenous almost periodic solution, which extend and include corresponding results obtained by Q. C. Lin (1999), F. D. Chen and X. X. Chen (2003), and Y. Q. Liu, S. L, Xie, and Z. D. Xie (1996).

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.

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