scholarly journals Strong singularities of attractive and repulsive type to 2n-order neutral differential equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yun Xin ◽  
Shaowen Yao ◽  
Ruichen Wang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Nonlinear Term ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Neutral Differential Equation ◽  
Coincidence Degree Theory

Abstract This paper is devoted to the existence of a positive periodic solution for a kind of 2n-order neutral differential equation with a singularity, where nonlinear term $g(t,x)$ g ( t , x ) has strong singularities of attractive and repulsive type at the origin. Our proof is based on coincidence degree theory.

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.

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.

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.

scholarly journals Existence of periodic solution for first order nonlinear neutral delay equations

2001 ◽  
Vol 14 (2) ◽  
pp. 189-194 ◽  
Author(s):  
Genqiang Wang ◽  
Jurang Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper by using the coincidence degree theory, sufficient conditions are given for the existence of periodic solutions of the first order nonlinear neutral delay differential equation.

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 Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Xiaoming Fan ◽  
Zhigang Wang ◽  
Fuquan Jiang
Keyword(s):  
Periodic Solution ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Functional Responses ◽  
Globally Exponential Stability ◽  
Impulsive Perturbations ◽  
Predator System

We explore the dynamics of a class of mutualism-competition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations. Sufficient conditions for existence of positive periodic solution are established by using a continuation theorem in coincidence degree theory, which have been extensively applied in studying existence problems in differential equations and difference equations. In addition, sufficient criteria are given for the global stability and the globally exponential stability of system by employing comparison principle and Lyapunov method.

scholarly journals Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1055 ◽  
Author(s):  
Manickam Iswarya ◽  
Ramachandran Raja ◽  
Grienggrai Rajchakit ◽  
Jinde Cao ◽  
Jehad Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Bam Neural Networks ◽  
Graph Theoretic

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

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