scholarly journals Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Kaihong Zhao
Keyword(s):  
Time Delay ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
System With Time Delay ◽  
Positive Almost Periodic Solutions

This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

scholarly journals Dynamics of two-species delayed competitive stage-structured model described by differential-difference equations

2019 ◽  
Vol 17 (1) ◽  
pp. 385-401 ◽  
Author(s):  
Sufang Han ◽  
Yaqin Li ◽  
Guoxin Liu ◽  
Lianglin Xiong ◽  
Tianwei Zhang
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Asymptotical Stability ◽  
Continuation Theorem ◽  
Global Asymptotical Stability ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
Positive Almost Periodic Solutions

Abstract Overf the last few years, by utilizing Mawhin’s continuation theorem of coincidence degree theory and Lyapunov functional, many scholars have been concerned with the global asymptotical stability of positive periodic solutions for the non-linear ecosystems. In the real world, almost periodicity is usually more realistic and more general than periodicity, but there are scarcely any papers concerning the issue of the global asymptotical stability of positive almost periodic solutions of non-linear ecosystems. In this paper we consider a kind of delayed two-species competitive model with stage structure. By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least one positive almost periodic solutions for the above model with nonnegative coefficients. Furthermore, the global asymptotical stability of positive almost periodic solution of the model is also studied. The work of this paper extends and improves some results in recent years. An example and simulations are employed to illustrate the main results of this paper.

scholarly journals Positive Almost Periodic Solutions for a Time-Varying Fishing Model with Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Xia Li ◽  
Yongkun Li ◽  
Chunyan He
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Almost Periodic Solution ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
Positive Almost Periodic Solutions

This paper is concerned with a time-varying fishing model with delay. By means of the continuation theorem of coincidence degree theory, we prove that it has at least one positive almost periodic solution.

scholarly journals Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yongzhi Liao ◽  
Yongkun Li ◽  
Xiaoyan Dou
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.

scholarly journals Existence of Positive Periodic Solutions for a Nonautonomous Generalized Predator-Prey System with Time Delay in Two-Patch Environment

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Huilan Wang ◽  
Zhengqiu Zhang ◽  
Weiping Zhou
Keyword(s):  
Periodic Solutions ◽  
Topological Degree ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System ◽  
System With Time Delay ◽  
Function Matrix

By using continuation theorem of coincidence degree theory, sufficient conditions of the existence of positive periodic solutions are obtained for a generalized predator-prey system with diffusion and delays. In this paper, we construct a V-function to make the prior estimation for periodic solutions, which makes the discussion more concise. Moreover, to compute the mapping's topological degree, a polynomial function matrix is constructed straightforwardly as a homotopic mapping for the generalized one, which improves the methods of computation on topological degree for a generalized mapping.

Almost Periodic Solution in a Lotka–Volterra Recurrent Neural Networks with Time-Varying Delays

2017 ◽  
Vol 18 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Li Yang ◽  
Zhouhong Li ◽  
Liyan Pang ◽  
Tianwei Zhang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
Existence And Stability

Abstract:By means of Mawhin’s continuation theorem of coincidence degree theory and Lyapunov function, some simple sufficient conditions are obtained for the existence and stability of a unique positive almost periodic solution of a delayed Lotka–Volterra recurrent neural networks. To a certain extent, the work in this paper corrects the defect of a recent paper. Finally, an example and simulations are given to illustrate the feasibility and effectiveness of the main result.

Dynamics of Almost Periodic Solution for a Delayed Facultative Mutualism Model Involving Negative Feedback Terms

2018 ◽  
Vol 19 (3-4) ◽  
pp. 309-320
Author(s):  
Li Yang ◽  
Zunguang Guo
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Analytical Techniques ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
Facultative Mutualism ◽  
Positive Almost Periodic Solution

AbstractBy using some new analytical techniques, modified inequalities and Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the boundedness of the solution and the existence of at least one positive almost periodic solution of a kind of two-species model of facultative mutualism with time delays. Further, the global asymptotic stability of the positive almost periodic solution of this model is also considered. Some examples and numerical simulations are also given to illustrate the main results of this paper.

MULTIPLE POSITIVE PERIODIC SOLUTIONS TO m-LAYER PERIODIC LOTKA–VOLTERRA NETWORK-LIKE MULTIDIRECTIONAL FOOD-CHAIN WITH HARVESTING TERMS

2011 ◽  
Vol 09 (01) ◽  
pp. 71-96 ◽  
Author(s):  
YONGKUN LI ◽  
KAIHONG ZHAO
Keyword(s):  
Periodic Solutions ◽  
Food Chain ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem

An m-layer peiodic Lotka–Volterra network-like multidirectional food-chain with harvesting terms is proposed in this paper. By applying Mawhin's continuation theorem of coincidence degree theory and some skills of the inequalities, sufficient conditions which guarantee the existence of [Formula: see text] positive periodic solutions of the system are obtained. An example is given to illustrate the effectiveness of our results.

scholarly journals On the existence of almost periodic solutions of impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms

2021 ◽  
Vol 7 (1) ◽  
pp. 925-938
Author(s):  
Li Wang ◽  
◽  
Hui Zhang ◽  
Suying Liu
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Continuation Theorem ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

<abstract><p>In this paper, by using the Mawhin's continuation theorem, some easily verifiable sufficient conditions are obtained to guarantee the existence of almost periodic solutions of impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms. Our result corrects the result obtained in <sup>[<xref ref-type="bibr" rid="b13">13</xref>]</sup>. An example and some remarks are given to illustrate the advantage of this paper.</p></abstract>

scholarly journals Positive Periodic Solutions in a Discrete Time Three Species Competition System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Changjin Xu ◽  
Yusen Wu
Keyword(s):  
Periodic Solutions ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Analogue ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Competition System

A periodic discrete time three species competition system is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous nonautonomous three species competition system is proposed. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of the model are obtained.

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