期刊：
Italian Journal of Pure and Applied Mathematics,2015年(35):705-716 ISSN：2239-0227
作者机构：
[Xu, Changjin] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, Hengyang, China
关键词：
Competition and cooperation model;Enterprise;Global stability;Stochastic perturbation
摘要：
This paper deals with a stochastic competition and cooperation model of two enterprises. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.
期刊：
IAENG International Journal of Applied Mathematics,2015年45(2):151-157 ISSN：1992-9978
作者机构：
[Xu C.] Department of Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, China;[Liao M.] School of Mathematics and Physics, University of South China, Hengyang, 421001, China
摘要：
In this paper, we study an Nicholson-type delay system with delays. New criteria for the boundedness and exponential stability of positive solutions of Nicholson-type system with time-varying delays are established by applying the fundamental solution matrix, inequality techniques and Lyapunov method. Two examples with their computer simulations are presented to illustrate the effectiveness of the theoretical findings. Our results are new and supplement some previously known ones.
期刊：
Journal of Computational and Theoretical Nanoscience,2015年12(10):3927-3935 ISSN：1546-1955
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, Hengyang, China;[Zhang, Qiming] College of Science, Hunan University of Technology, Zhuzhou, China
通讯机构：
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, China
摘要：
This paper is concerned with the existence and exponential stability of anti-periodic solutions of shunting inhibitory cellular neural networks with impulses and continuously distributed delays. Applying Krasnoselski's fixed point theorem, inequality techniques and Lyapunov method, sufficient conditions which ensure the existence and exponential stability of anti-periodic solutions of shunting inhibitory neural networks are presented. An example with its numerical simulations is given to illustrate our main results. Our results are new and supplement some previously known ones.
摘要：
In this paper, dynamical behaviors for a competition and cooperation model of two enterprises with two delays are investigated. By choosing the diverse delay as a bifurcation parameter, we show that the complex Hopf bifurcation phenomenon at the positive equilibrium of the system can occur as the diverse delay crosses some critical values. Finally, some numerical simulations supporting our theoretical results and the economic meaning of the model are also presented.
期刊：
International Journal of Innovative Computing, Information and Control,2014年10(5):1747-1764 ISSN：1349-4198
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Huaxi District, Guiyang, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, No. 28. Changsheng West Road, Hengyang, China
通讯机构：
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Huaxi District, Guiyang, China
关键词：
Discrete delay;Hopf bifurcation;Periodic solution;Stability;Three-species Lotka-Volterra system
关键词：
Ring network;stability;Hopf bifurcation;discrete delay;periodic solution
摘要：
In this paper, a five-neuron model with discrete delays is considered, where the time delays are regarded as parameters. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. 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. Finally, numerical simulations supporting the theoretical analysis are presented.
摘要：
This article is concerned with the local stability of a positive equilibrium and the Hopf bifurcation of a delayed three-species food-chain system with the Holling type-II functional response. Some new sufficient conditions ensuring the local stability of a positive equilibrium and the existence of Hopf bifurcation for the system are established. Some explicit formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions using the normal form theory and the centre manifold theory. Numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are included.
期刊：
Discrete Dynamics in Nature and Society,2013年2013 ISSN：1026-0226
通讯作者：
Liao, Maoxin
作者机构：
[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liao, Maoxin] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
摘要：
In this note, we consider global asymptotic stability of the following nonlinear difference equation x(n) = (Pi(v)(i=1)(x(n-ki)(beta i)+1)+Pi(v)(i=1)(x(n-ki)(beta i)-1))/(Pi(v)(i-1)(x(n-ki)(beta i)+1)-Pi(v)(i-1)(x(n-ki)(beta i)-1)), n = 0, 1, ... , where k(i) is an element of N (i = 1, 2, ... , v), v >= 2, beta(1) is an element of [-1,1], beta(2), beta(3), ..., beta(v) is an element of (-infinity,+infinity), x(-m), x(-m+1), ... , x(-1) is an element of (0,infinity), and m = max(1 <= i <= v){k(i)}. Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al. (2007).
期刊：
Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis,2012年19(6):675-691 ISSN：1201-3390
通讯作者：
Liao, M.
作者机构：
[Liao M.] School of Mathematics and Physics, University of South China, Hengyang 421001, China;[Xu C.] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance And, Economics, Guiyang 550004, China
通讯机构：
[Liao, M.] S;School of Mathematics and Physics, University of South China, China
期刊：
Asian-European Journal of Mathematics,2012年5(2):1250031 ISSN：1793-5571
通讯作者：
Xu, C.
作者机构：
[Maoxin Liao] School of Mathematics and Physics, Nanhua University, Hengyang 421001, P. R. China;[Changjin Xu] Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550004, P. R. China
通讯机构：
[Xu, C.] G;Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou University of Finance and Economics, China
关键词：
Predator–prey;stage-structure;periodic solution;Beddington–DeAngelis functional response;Holling IV functional response;topological degree
