scholarly journals Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Rouzimaimaiti Mahemuti ◽  
Zhidong Teng
Keyword(s):  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Competitive Systems ◽  
Volterra Systems ◽  
Special Cases

We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

scholarly journals Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tursuneli Niyaz ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Feedback Controls ◽  
Volterra Systems

This paper studies a class of periodicnspecies cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.

scholarly journals Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Lyapunov Function ◽  
Periodic Solutions ◽  
Function Method ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Facultative Mutualism ◽  
Lyapunov Function Method

Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

scholarly journals Existence and Global Attractivity of Positive Periodic Solutions for a Two-Species Competitive System with Stage Structure and Impulse

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Changjin Xu ◽  
Daxue Chen
Keyword(s):  
Periodic Solution ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Competitive System

A class of nonautonomous two-species competitive system with stage structure and impulse is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantee the existence of at least a positive periodic solution, and, by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Finally, an illustrative example is given to demonstrate the correctness of the obtained results.

scholarly journals Multiple Periodic Solutions of a Nonautonomous Plant-Hare Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongfei Gao ◽  
P. J. Y. Wong ◽  
Y. H. Xia ◽  
Xiaoqing Yuan
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
New Technique ◽  
Positive Periodic Solutions ◽  
Multiple Periodic Solutions

Based on Mawhin's coincidence degree theory, sufficient conditions are obtained for the existence of at leasttwopositive periodic solutions for a plant-hare model with toxin-determined functional response (nonmonotone). Some new technique is used in this paper, because standard arguments in the literature are not applicable.

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.

scholarly journals Existence of positive periodic solutions for a class of in-host MERS-CoV infection model with periodic coefficients

2021 ◽  
Vol 7 (2) ◽  
pp. 3083-3096
Author(s):  
Tuersunjiang Keyoumu ◽  
◽  
Wanbiao Ma ◽  
Ke Guo
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Positive Periodic Solutions ◽  
Periodic Coefficients ◽  
Autonomous Case

<abstract><p>In this paper, a dynamic model of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) with periodic coefficients is proposed and studied. By using the continuation theorem of the coincidence degree theory, we obtain some sufficient conditions for the existence of positive periodic solutions of the model. The periodic model degenerates to an autonomous case, and our conditions can be degenerated to the basic reproductive number $ R_0 &gt; 1 $. Finally, we give some numerical simulations to illustrate our main theoretical results.</p></abstract>

PERIODICITY IN AN STAGE-STRUCTURED THREE-SPECIES PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS AND HOLLINF IV FUNCTIONAL RESPONSE

2012 ◽  
Vol 05 (02) ◽  
pp. 1250031
Author(s):  
Changjin Xu ◽  
Maoxin Liao
Keyword(s):  
Functional Response ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Sufficient Condition ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Prey System

In this paper, by using the continuation theorem of coincidence degree theory, a sufficient condition of existence of positive periodic solutions is obtained for an stage-structured three-species predator–prey system with Beddington–DeAngelis and Holling IV functional response. By constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Our result is a good complement to the earlier publications.

scholarly journals Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Liu Yang ◽  
Zhenghui Gao ◽  
Yunhui Zeng
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Predator Population ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.

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