一类具周期裂解免疫反应的HIV感染模型正周期解的存在性
作者：
王会兰;廖新元;朱惠延
期刊：
南华大学学报(自然科学版) ,2012年26(1):44-47 ISSN：1673-0062
作者机构：
南华大学数理学院,湖南衡阳,421001;[朱惠延; 廖新元; 王会兰] 南华大学
关键词：
HIV感染;裂解免疫反应;正周期解;拓扑度
摘要：
考虑了HIV感染系统中免疫细胞对感染细胞的周期裂解作用，建立起具有免疫饱和效应的时滞微分方程模型，运用非线性泛函分析中的拓扑度理论，得到了系统存在正周期解的充分条件．
语种：
中文
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具免疫应答时滞乙肝病毒的数学模型
作者：
王光菊;杜鹏;廖新元
期刊：
三明学院学报 ,2012年29(2):9-16 ISSN：1673-4343
作者机构：
南华大学数理学院,湖南衡阳,421001;[杜鹏; 王光菊; 廖新元] 南华大学
关键词：
乙肝病毒;免疫应答;Lyapunov函数;稳定性分析;时滞微分方程
摘要：
据统计,世界有1/3的人口曾经感染乙肝病毒,约有3.5亿人是HBV携带者。如何预防和治疗乙肝一直是社会关注的焦点和医学与数学等交叉学科的重要课题。基于Nowak模型,建立了具免疫时滞因素HBV感染时滞微分方程模型,对该模型的动力学进行了分析,并应用Routh-Hurwitze定理及Lyapunov-Lasalle定理讨论了该模型平衡点的稳定性,分析了免疫时滞对系统动力学性质产生的影响。数值模拟验证了所得到的结果。
语种：
中文
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Traveling wavefronts of a prey–predator diffusion system with stage-structure and harvesting
作者：
Liao, Xinyuan* ;Chen, Yuming;Zhou, Shengfan
期刊：
Journal of Computational and Applied Mathematics ,2011年235(8):2560-2568 ISSN：0377-0427
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Chen, Yuming] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada.;[Zhou, Shengfan] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.
通讯机构：
[Liao, Xinyuan] U;Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Diffusion;Preypredator system;Stability;Stage-structure;Traveling wavefront
摘要：
From a biological point of view, we consider a prey-predator-type free diffusion fishery model with stage-structure and harvesting. First, we study the stability of the nonnegative constant equilibria. In particular, the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulation. Then, employing the upper and lower solution method, we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system. Numerical simulation is also carried out to illustrate the main result. ©2010 Elsevier B.V. All rights reserved.
语种：
英文
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重物落水后运动过程的数学模型分析
作者：
王光菊;吁锤;廖新元
期刊：
南华大学学报(自然科学版) ,2011年25(2):45-48 ISSN：1673-0062
作者机构：
南华大学数理学院,湖南衡阳,421001;[王光菊; 吁锤; 廖新元] 南华大学
关键词：
运动方程;粘滞阻力;二分法;模型试验
摘要：
针对封堵溃口问题，根据流体力学理论，建立了重物落水后运动过程的数学模型，利用小型试验获取相关数据的方法进行研究，用该模型对实验的工况进行了计算，并对模型和实验进行了分析和评价．通过实例，验证了该模型较好地模拟了大坝溃决后的重物落水后的运动过程，模型结果可以为溃坝洪水风险提供科学依据．
语种：
中文
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具常数输入有饱和传染率和垂直传染的SEIR模型
作者：
陈建娟;廖新元;王光菊
期刊：
江苏师范大学学报(自然科学版) ,2011年29(4):16-20 ISSN：2095-4298
作者机构：
南华大学数理学院,湖南衡阳,421001;[王光菊; 陈建娟; 廖新元] 南华大学
关键词：
饱和传染率;垂直传染;Hurwitz判据
摘要：
考虑一类具常数输入有饱和传染率和垂直传染的SEIR模型,通过计算得到了基本再生数R0,利用线性化方法、Hurwitz判据分析了平衡点的局部稳定性,根据Lozinskil测度分析了系统不存在周期轨道,并由Poincare-Ben-dixson性质、比较法等得到了无病平衡点和地方病平衡点的全局渐近稳定性.
语种：
中文
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Existence of traveling wavefronts in a cooperative systems with discrete delays
作者：
Liao, Xinyuan* ;Tang, Xianhua;Zhou, Shengfan
期刊：
Applied Mathematics and Computation ,2009年215(5):1806-1812 ISSN：0096-3003
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Tang, Xianhua] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China.;[Zhou, Shengfan] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.
通讯机构：
[Liao, Xinyuan] U;Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Lotka-Volterra cooperative system;Traveling wave front;Upper and lower solution;Monotone iteration technique
摘要：
In this paper, we consider an important Lotka-Volterra model describing a two-species cooperative system with diffusive and discrete delays, and investigate the existence of traveling wavefronts by some mathematics tools including the monotone iteration technique as well as the upper and lower solution method. The results obtained can be seen as a generalization of previous results. © 2009 Elsevier Inc. All rights reserved.
语种：
英文
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On the discrete-time multi-species competition–predation system with several delays
作者：
Liao, Xinyuan* ;Zhou, Shengfan;Raffoul, Youssef N.
期刊：
Applied Mathematics Letters ,2008年21(1):15-22 ISSN：0893-9659
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Nanhua Univ, Sch Math & Phys, Henyang 421001, Hunan, Peoples R China.;[Liao, Xinyuan] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.;[Zhou, Shengfan] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.;[Raffoul, Youssef N.] Univ Dayton, Dept Math, Dayton, OH 45469 USA.
通讯机构：
[Liao, Xinyuan] N;Nanhua Univ, Sch Math & Phys, Henyang 421001, Hunan, Peoples R China.
关键词：
permanence;delayed;discrete-time;competition-predation system;non-autonomous;multi-species;LOTKA-VOLTERRA SYSTEM;GLOBAL ATTRACTIVITY;PERIODIC-SOLUTIONS;PREY SYSTEM;ASYMPTOTIC STABILITY;DEVIATING ARGUMENTS;PERMANENCE;PERSISTENCE;FEEDBACK
摘要：
In this work, we study a discrete-time multi-species ecological competition-predation system with several delays. By a new method of difference inequality, it is shown that the system is permanent under some appropriate conditions. Moreover, we give an example to illustrate the feasibility of our result. (c) 2007 Elsevier Ltd. All rights reserved.
语种：
英文
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Permanence and global stability in a discrete n-species competition system with feedback controls
作者：
Liao, Xinyuan* ;Zhou, Shengfan;Chen, Yuming
期刊：
Nonlinear Analysis: Real World Applications ,2008年9(4):1661-1671 ISSN：1468-1218
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Liao, Xinyuan] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.;[Zhou, Shengfan] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.;[Chen, Yuming] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada.
通讯机构：
[Liao, Xinyuan] U;Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
permanence;nonautonomous;Lotka-Volterra discrete system;feedback control;global stability
摘要：
In this paper, we investigate the following discrete n-species competition system with feedback controls:x<inf>i</inf> (k + 1) = x<inf>i</inf> (k) exp fenced(b<inf>i</inf> (k) - underover(∑, j = 1, n) a<inf>ij</inf> (k) x<inf>j</inf> (k) - underover(∑, j = 1, j ≠i, n) c<inf>ij</inf> (k) x<inf>i</inf> (k) x<inf>j</inf> (k) - d<inf>i</inf> (k) u<inf>i</inf> (k)),Δu<inf>i</inf> (k) = r<inf>i</inf> (k) - e<inf>i</inf> (k) u<inf>i</inf> (k) + f<inf>i</inf> (k) x<inf>i</inf> (k), i = 1, 2, ..., n,which describes the effect of toxic substances and age structures simultaneously. Some sufficient conditions are established on the permanence and the global stability of the system. These results are also applied to some special cases. ©2007 Elsevier Ltd. All rights reserved.
语种：
英文
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Permanence of species in nonautonomous discrete Lotka–Volterra competitive system with delays and feedback controls
作者：
Liao, Xinyuan;Ottyang, Zigen;Zhou, Shengfan
期刊：
Journal of Computational and Applied Mathematics ,2008年211(1):1-10 ISSN：0377-0427
通讯作者：
Liao, XY
作者机构：
[Liao, Xinyuan; Ottyang, Zigen] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Liao, Xinyuan] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.;[Zhou, Shengfan] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.
通讯机构：
[Liao, XY ] ;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
positive solution;delays;Lotka-Volterra discrete system;permanence;N-species;with feedback controls;POSITIVE PERIODIC-SOLUTIONS;FOOD-CHAIN MODEL;GLOBAL ATTRACTIVITY;TIME DELAYS;EXISTENCE;STABILITY;EQUATIONS;EXTINCTION
摘要：
A nonautonomous N-species discrete Lotka-Volterra competitive system of difference equations with delays and feedback controls is considered. New sufficient conditions are obtained for the permanence of this discrete system. The results indicate that one can choose suitable controls to make the species coexistence in the long run. Moreover, we give some examples to illustrate the feasibility of our result which can be well suited for computational purposes. (C) 2006 Elsevier B.V. All rights reserved.
语种：
英文
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Permanence for a discrete time Lotka–Volterra type food-chain model with delays
作者：
Liao, Xinyuan* ;Zhou, Shengfan;Chen, Yuming
期刊：
Applied Mathematics and Computation ,2007年186(1):279-285 ISSN：0096-3003
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.;Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada.
通讯机构：
[Liao, Xinyuan] N;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
permanence;delay;discrete Lotka-Volterra system;food-chain;coexistence;PREDATOR-PREY SYSTEM;GLOBAL STABILITY;PERIODIC-SOLUTIONS;ATTRACTIVITY;PERSISTENCE
摘要：
Considered is a delayed discrete time Lotka-Volterra type food-chain model. Sufficient conditions are established for the permanence and the feasibility of the obtained results are illustrated with an example. © 2006 Elsevier Inc. All rights reserved.
语种：
英文
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On permanence and global stability in a general Gilpin–Ayala competition predator–prey discrete system
作者：
Liao, Xinyuan* ;Zhou, Shengfan;Chen, Yuming
期刊：
Applied Mathematics and Computation ,2007年190(1):500-509 ISSN：0096-3003
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Nanhua Univ, Sch Phys & Mat, Hengyang 421001, Hunan, Peoples R China.;Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.;Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.;Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada.
通讯机构：
[Liao, Xinyuan] N;Nanhua Univ, Sch Phys & Mat, Hengyang 421001, Hunan, Peoples R China.
关键词：
permanence;discrete;Gilpin-Ayala competition predator-prey system;stability;MODEL;DIFFUSION
摘要：
In this paper, we propose a discrete multispecies general Gilpin-Ayala competition predator-prey model. By using new difference inequality and developing the analysis technique of Chen and Zhou [Y. Chen, Z. Zhou, Stable periodic solution of a discrete periodic Lotka-Volterra competition system, J. Math. Anal. Appl. 277 (2003) 358-366], sufficient conditions are established for the permanence and the global stability. An example shows the feasibility of our results. © 2007 Elsevier Inc. All rights reserved.
语种：
英文
展开
Permanence and stability of equilibrium for a two-prey one-predator discrete model
作者：
Liao, Xinyuan* ;Ouyang, Zigen;Zhou, Shengfan
期刊：
Applied Mathematics and Computation ,2007年186(1):93-100 ISSN：0096-3003
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Nanhua Univ Hengyang, Sch Math & Phys, Hunan 421001, Peoples R China.;Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.
通讯机构：
[Liao, Xinyuan] N;Nanhua Univ Hengyang, Sch Math & Phys, Hunan 421001, Peoples R China.
关键词：
predator-prey system;discrete model;stability;permanence;VOLTERRA COMPETITION SYSTEM;GLOBAL STABILITY;PREY SYSTEM;UNIFORM PERSISTENCE;FUNCTIONAL-RESPONSE;DELAYS
摘要：
In this letter, a predator-prey system of two-prey one-predator discrete model is investigated. It is proved that the system is permanence under some appropriate conditions. By Jacobian matrix method, a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system. Meanwhile, we give a suitable example for supporting our theoretical result. (c) 2006 Elsevier Inc. All rights reserved.
语种：
英文
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On a stoichiometric two predators on one prey discrete model
作者：
Liao, Xinyuan* ;Zhou, Shengfan;Ouyang, Zigen
期刊：
Applied Mathematics Letters ,2007年20(3):272-278 ISSN：0893-9659
通讯作者：
Liao, Xinyuan
作者机构：
[Liao, Xinyuan] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;Shanghai Univ, Dept Mat Sci, Shanghai 200444, Peoples R China.;Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.
通讯机构：
[Liao, Xinyuan] N;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
stoichiometry;discrete model;predator-prey model;boundedness;global attractivity;SYSTEMS;DELAY
摘要：
In this letter, we first propose a discrete analogue of a continuous time predator-prey system, which models the dynamics of two predators on one prey [I. Loladze, Y. Kuang, J. Elser, W.F. Fagan, Competition and stoichiometry: Coexistence of two predators on one prey, Theor. Popul. Biol. 65 (2004) 1-15]. Then, we study the dynamics of this discrete model. We establish results on boundedness and global attractivity. Finally, several numerical simulations are given to support the theoretical results. © 2006 Elsevier Ltd. All rights reserved.
语种：
英文
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The dynamic behavior of N-species cooperation system with continuous time delays and feedback controls
作者：
Chen, Fengde;Liao, Xinyuan;Huang, Zhenkun
期刊：
Applied Mathematics and Computation ,2006年181(2):803-815 ISSN：0096-3003
通讯作者：
Chen, FD
作者机构：
[Chen, Fengde] College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China;[Huang, Zhenkun] School of Sciences, Jimei University, Xiamen, Fujian 361021, China;[Liao, Xinyuan] Department of Mathematics, Shanghai University, Shanghai, 200444, China;[Liao, Xinyuan] School of Mathematics and Physics, Nanhua University, Hengyang, Hunan 421001, China
通讯机构：
[Chen, FD ] ;Fuzhou Univ, Coll Math & Comp Sci, Fujian 350002, Peoples R China.
关键词：
cooperation system;permanence;periodic solution;almost periodic solution;global attractivity;feedback controls;POSITIVE PERIODIC-SOLUTIONS;VOLTERRA COMPETITION SYSTEM;PERMANENCE;STABILITY;EXISTENCE;MODEL
摘要：
In this paper, we consider a N-species cooperation system with continuous time delays and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain sufficient conditions which guarantee the existence, uniqueness and stability of a positive periodic solution. For the almost periodic case, by using the Razumikhin type theorem, we obtain the sufficient conditions which guarantee the existence of a positive almost periodic solution of the system. © 2006 Elsevier Inc. All rights reserved.
语种：
英文
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On asymptotic stability of delay-difference systems
作者：
Liao, Xin-Yuan* ;Zhu, Hui-Yan;Chen, Feng-de
期刊：
Applied Mathematics and Computation ,2006年176(2):759-767 ISSN：0096-3003
通讯作者：
Liao, Xin-Yuan
作者机构：
[Liao, Xin-Yuan] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.;Nanhua Univ, Sch Math & Phys, Hunan 421001, Peoples R China.;Fuzhou Univ, Sch Math & Comp Sci, Fuzhou 350002, Fujiang, Peoples R China.
通讯机构：
[Liao, Xin-Yuan] S;Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.
关键词：
asymptotic stability;stability criteria;Lyapunov function;delay-difference equations;matrix inequalities;LINEAR NEUTRAL SYSTEMS;DISCRETE-SYSTEMS;EQUATIONS;BOUNDEDNESS;CRITERIA
摘要：
In this paper, we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay-difference systems by using a discrete version of the second Lyapunov method. Our results can be well suited for computational purposes. © 2005 Elsevier Inc. All rights reserved.
语种：
英文
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Convergent and divergent solutions of a discrete nonautonomous Lotka-Volterra model
作者：
Xin-yuan Liao;Sui Sun Cheng
期刊：
Tamkang Journal of Mathematics ,2005年36(4):337-344 ISSN：0049-2930
通讯作者：
Liao, X.-Y.
作者机构：
School of Mathematics and Physics, Nanhua University Hengyang, Hunan 421001, China;Department of Mathematics, Tsing Hua University, Hsinchu, 30043, Taiwan
通讯机构：
School of Mathematics and Physics, Nanhua University Hengyang, China
关键词：
Asymptotic behavior;Fixed point theorems;Lotka-Volterra competition system;Positive solutions
摘要：
In this paper, a discrete nonautonomous $m$-species Lotka-Volterra system is investigated. By using fixed point theorems, a set of simple and easily verifiable conditions are given for the existence of convergent or divergent positive solutions.
语种：
英文
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Convergence and periodicity of solutions for a class of delay difference equations
作者：
Zhu, HY;Huang, LH* ;Liao, XY
期刊：
Computers & Mathematics with Applications ,2004年48(10-11):1477-1484 ISSN：0898-1221
通讯作者：
Huang, LH
作者机构：
[Huang, LH] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;Nanhua Univ, Coll Math Phys, Hunan 421001, Peoples R China.
通讯机构：
[Huang, LH] H;Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
关键词：
Convergence;Difference equation;Periodicity
摘要：
We derive a class of delay difference equations with piecewise constant nonlinearity. The convergence of solutions and the existence of asymptotically stable periodic solutions are investigated, for such a class of difference equations. © 2004 Elsevier Ltd. All rights reserved.
语种：
英文
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一阶中立型微分方程解的振动性(英文)
作者：
廖新元;欧阳自根
期刊：
广西师范大学学报(自然科学版) ,2003年21(3):52-55 ISSN：1001-6600
作者机构：
南华大学数理学院,湖南,衡阳,421001
关键词：
positive and negative coefficients;neutral differential equation;oscillation;eventually positive solution
摘要：
New sufficient conditions for the oscillation are obtained for all solutions of a class of first order neutral differential equations with positive and negative coefficients.
语种：
英文
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高等数学课程建设探索与实践
作者：
朱惠延;欧阳自根;刘亚春;廖基定;廖新元
期刊：
数学理论与应用 ,2003年(04):21-23 ISSN：1006-8074
作者机构：
南华大学数理学院;南华大学数理学院 衡阳;421001
关键词：
高等数学课程建设;师资队伍建设;教学方法;手段改革;双语教学;第二课堂
摘要：
本文探索了高等数学课程应适应当今教育要求 ,达到培养学生数学素质和能力的建设思路 ,总结了高等数学课程建设在师资队伍建设 ,教学方法、手段改革 ,高等数学双语教学及开展第二课堂等方面所取得的成果
语种：
中文
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