期刊：
International Journal of Mathematics and Mathematical Sciences,2011年2011(17):970763:1-970763:18 ISSN：0161-1712
通讯作者：
Xu, C.
作者机构：
Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, China;School of Mathematics and Physics, Nanhua University, Hengyang 421001, China
通讯机构：
Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, China
摘要：
In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.
摘要：
In this paper, a class of delayed Lokta-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also provided. Finally, main conclusions are given.
摘要：
In this paper, a six-neuron BAM neural network model with discrete delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the model is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form method and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are given. In this paper, a six-neuron BAM neural network model with discrete delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the model is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form method and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are given.
摘要：
In this paper, we consider a ratio-dependent predator-prey system with diffusion. And we mainly discuss the following problems: (1) stability and Hopf bifurcation analysis of the positive equilibrium for the reduced ODE system; (2) Diffusion-driven instability of the equilibrium solution; (3) Hopf bifurcations for the corresponding diffusion system with homogeneous Neumann boundary conditions. In order to verify our theoretical results, some numerical simulations are also included, respectively. (C) 2010 Elsevier Ltd. All rights reserved.
期刊：
IAENG International Journal of Applied Mathematics,2011年41(3):191-198 ISSN：1992-9978
通讯作者：
Xu, C.
作者机构：
[Xu C.] Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang, China;[Iiao M.] School of Mathematics and Physics, Nanhua University, Hengyang, 421001, China
通讯机构：
[Xu, C.] G;Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, China
摘要：
In this paper, a special SEIR epidemic model with nonlinear incidence rates is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation for justifying the theoretical analysis are also presented. Finally, biological explanations and main conclusions are given.
期刊：
Journal of Applied Mathematics and Computing,2011年35(1-2):63-71 ISSN：1598-5865
通讯作者：
Liao, M.(maoxinliao@163.com)
作者机构：
School of Mathematics and Physics, University of South China, Hengyang, P.R. China;[Tang, Xianhua; Xu, Changjin] School of Mathematical Sciences and Computing Technology, Central South University, Changsha, P.R. China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, Hengyang, P.R. China<&wdkj&>School of Mathematical Sciences and Computing Technology, Central South University, Changsha, P.R. China
通讯机构：
[Maoxin Liao] S;School of Mathematics and Physics, University of South China, Hengyang, P.R. China<&wdkj&>School of Mathematical Sciences and Computing Technology, Central South University, Changsha, P.R. China
关键词：
Global asymptotic stability;Persistence;Positive equilibrium point;Rational difference equation
摘要：
In this note we consider the following higher order rational difference equations
$$x_{n}=1+\frac{(1-x_{n-k})(1-x_{n-l})(1-x_{n-m})}{x_{n-k}+x_{n-l}+x_{n-m}},\quad n=0,1,\ldots,$$
where 1≤k<l<m, and the initial values x
−m
,x
−m+1,…,x
−1 are positive numbers. We give some sufficient conditions for the persistence of positive solutions for the above equation, and prove that the positive equilibrium point of this equation is globally asymptotically stable.
