scholarly journals Almost Periodic Solution of a Discrete Commensalism System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Yalong Xue ◽  
Xiangdong Xie ◽  
Fengde Chen ◽  
Rongyu Han
Keyword(s):  
Periodic Solution ◽  
Comparison Theorem ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Discrete Lyapunov Functional ◽  
Globally Attractive

A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.

scholarly journals ALMOST-PERIODIC SOLUTIONS FOR AN ECOLOGICAL MODEL WITH INFINITE DELAYS

2007 ◽  
Vol 50 (1) ◽  
pp. 229-249 ◽  
Author(s):  
Yonghui Xia ◽  
Jinde Cao
Keyword(s):  
Periodic Solution ◽  
Lyapunov Functional ◽  
Ecological Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Volterra Model ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Infinite Delays ◽  
Dominated Convergence

AbstractBy using Lebesgue’s dominated convergence theorem and constructing a suitable Lyapunov functional, we study the following almost-periodic Lotka–Volterra model with $M$ predators and $N$ prey of the integro-differential equations\begin{alignat*}{2} \dot{x}_i(t)\amp=x_i(t)\biggl[b_i(t)-a_{ii}(t)x_i(t)-\sum_{k=1,k\neq i}^{N}a_{ik}(t)\int_{-\infty}^tH_{ik}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma\\ \amp\hskip45mm-\sum_{l=1}^{M}c_{il}(t)\int_{-\infty}^tK_{il}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad i\amp=1,2,\dots,N,\\ \dot{y}_j(t)\amp=y_j(t)\biggl[-r_j(t)-e_{jj}(t)y_j(t) +\sum_{k=1}^{N}d_{jk}(t)\int_{-\infty}^tP_{jk}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma \\ \amp\hskip45mm-\sum_{l=1,l\neq j}^{M} e_{jl}(t)\int_{-\infty}^tQ_{jl}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad j\amp=1,2,\dots,M. \end{alignat*}Some sufficient conditions are obtained for the existence of a unique almost-periodic solution of this model. Several examples show that the obtained criteria are new, general and easily verifiable.

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 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.

NEW CRITERIA OF ALMOST PERIODIC SOLUTION FOR BAM NEURAL NETWORKS WITH DELAYS AND IMPULSIVE EFFECTS

2007 ◽  
Vol 17 (05) ◽  
pp. 395-406 ◽  
Author(s):  
JUN CHEN ◽  
BAOTONG CUI ◽  
YAN JI
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Time Varying ◽  
Almost Periodic ◽  
Inequality Technique ◽  
New Criteria

This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.

Dynamics of an N-Species Gilpin–Ayala Impulsive Competition System

2019 ◽  
Vol 20 (7-8) ◽  
pp. 737-746
Author(s):  
Libo Wang ◽  
Guigui Xu
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Asymptotical Stability ◽  
Global Asymptotical Stability ◽  
Almost Periodic ◽  
Competition System

AbstractIn this paper, we consider an N-species Gilpin–Ayala impulsive competition system. By using comparison theorem, Lyapunov functional, and almost periodic functional hull theory of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence, global asymptotical stability, and almost periodic solution of the model. Our results extend some previously known results. The method used in this paper provides a possible method to study the permanence, global asymptotical stability, and almost periodic solution of the models with impulsive perturbations in biological populations.

scholarly journals Permanence and Almost Periodic Solutions of a Discrete Ratio-Dependent Leslie System with Time Delays and Feedback Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-31 ◽  
Author(s):  
Gang Yu ◽  
Hongying Lu
Keyword(s):  
Time Delays ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Positive Almost Periodic Solution ◽  
Ratio Dependent ◽  
Globally Attractive ◽  
Leslie System

We consider a discrete almost periodic ratio-dependent Leslie system with time delays and feedback controls. Sufficient conditions are obtained for the permanence and global attractivity of the system. Furthermore, by using an almost periodic functional Hull theory, we show that the almost periodic system has a unique globally attractive positive almost periodic solution.

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 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.

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