scholarly journals Existence of positive periodic solution of a periodic cooperative model with delays and impulses

2006 ◽  
Vol 2006 ◽  
pp. 1-16
Author(s):  
Yongkun Li ◽  
Wenya Xing
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Mawhin’S Continuation Theorem ◽  
Cooperative Model

Sufficient conditions are obtained for the existence of at least one positive periodic solution of a periodic cooperative model with delays and impulses by using Mawhin's continuation theorem of coincidence degree theory.

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.

Periodic Solution of a Class Predator-Prey System with Rate Stocking and Time Delay

2013 ◽  
Vol 291-294 ◽  
pp. 2412-2415
Author(s):  
Hui Li ◽  
Yi Fei Wang
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Periodic System ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Coincidence Degree Theory ◽  
Predator Prey ◽  
Prey System

In this paper, we investigate of a class of predator-prey system with rate stocking and time delay, the existence positive periodic solution by using coincidence degree theory. We obtain the sufficient conditions which guarantee existence of the positive periodic solution of the periodic system. Some new results obtained.

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.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF PERIODIC SOLUTION OF A CLASS OF IMPULSIVE NETWORKS WITH INFINITE DELAYS

2007 ◽  
Vol 17 (01) ◽  
pp. 35-42 ◽  
Author(s):  
YONGHUI XIA ◽  
JINDE CAO ◽  
MUREN LIN
Keyword(s):  
Periodic Solution ◽  
Exponential Stability ◽  
Lyapunov Functions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Mawhin’S Continuation Theorem ◽  
Neuron Networks ◽  
Infinite Delays

Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of a class of impulsive tow-neuron networks with variable and unbounded delays. The approaches are based on Mawhin's continuation theorem of coincidence degree theory and Lyapunov functions.

POSITIVE PERIODIC SOLUTION FOR A GAUSE-TYPE RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

2008 ◽  
Vol 01 (03) ◽  
pp. 339-354 ◽  
Author(s):  
XIAOQUAN DING ◽  
YUANYUAN WANG
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Continuation Theorem ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent ◽  
System With Time Delay

A two-species Gause-type ratio-dependent predator-prey system with time delay in a two-patch environment is investigated. By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of periodic solution for the system. As corollaries, some applications are listed. In particular, our results extend and improve some known results.

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.

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 Existence and global exponential stability of periodic solution of high-order Cohen-Grossberg neural network with impulses

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Jing Liu
Keyword(s):  
Neural Network ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
High Order ◽  
Continuation Theorem ◽  
Mawhin’S Continuation Theorem

AbstractSufficient conditions are obtained for the existence and global exponential stability of periodic solution of high-order Cohen-Grossberg neural network with impulses by using Mawhin’s continuation theorem of coincidence degree and by means of a method based differential inequality.

scholarly journals Multiple Periodic Solutions to a Kind of Lotka-Volterra Food-Chain System with Delays and Impulses on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-29
Author(s):  
Kaihong Zhao ◽  
Liang Ding ◽  
Fengzao Yang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Food Chain ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Mawhin’S Continuation Theorem ◽  
Chain System ◽  
Multiple Periodic Solutions

By using Mawhin’s continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least 2n periodic solutions for a kind of n-species Lotka-Volterra food-chain system with delays and impulses on time scales. One example is given to illustrate the effectiveness of our results.

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