关键词：
Bifurcation control;Competitive web site model;Internet;Stability;Hopf bifurcation;Fractional order;Delay
摘要：
In today's society, the Internet has become an important tool of our life due to its potential applications in various areas such as economics, industry, agriculture, medical and health care, and information processing. To understand and grasp the law of the Internet, many competitive web site models of the Internet and some phenomena related to World Wide Web have been investigated systematically. However, many scholars only study the integer-order competitive web site models of the Internet. Up to now, there are few papers that focus on the dynamics of fractional-order competitive web site models of Internet, which possess memory property. In this paper, we are concerned with the stability and the existence of Hopf bifurcation of a fractional-order competitive web site model of Internet. By choosing the time delay as parameter and applying the Routh-Hurwitz criteria, we will establish a new sufficient condition guaranteeing the stability and the existence of Hopf bifurcation for fractional-order competitive web site model of Internet. The research reveals that fractional order and the delay play a key role in describing the stability and Hopf bifurcation of the considered system. Computer simulations are implemented to support the analytic results. Finally, a simple conclusion is presented. The theoretical findings of this article have a great significance in handling the competition dynamics among different web sites.
摘要：
This paper deals with a stochastic two-species competitive model. 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：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2016年26(7):1650119 ISSN：0218-1274
通讯作者：
Wang, Qi-Ru
作者机构：
[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Wang, Qi-Ru] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China.
通讯机构：
[Wang, Qi-Ru] S;Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China.
摘要：
In this paper, the dynamic properties for a Brusselator-type system with diffusion are investigated. By employing the theory of Hopf bifurcation for ordinary and partial differential equations, we mainly obtain some conditions of the stability and Hopf bifurcation for the ODE system, diffusion-driven instability of the equilibrium solution, and the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions for the PDE system. Finally, some numerical simulations are presented to verify our results.
摘要：
In this paper, we investigate a class of stochastic shunting inhibitory cellular neural networks with time-varying delays. Applying integral inequality, some sufficient conditions on the existence and p-exponential stability of periodic solutions for stochastic shunting inhibitory cellular neural networks with time-varying delays are established. An example is presented to illustrate our main theoretical findings. Our results are new and complementary to previously known studies.
摘要：
This paper is concerned with the shunting inhibitory cellular neural networks with time-varying delays. Under some suitable conditions, we establish some criteria on the existence and global exponential stability of the almost automorphic solutions of the networks. Numerical simulations are given to support the theoretical findings.
期刊：
Journal of Computational and Theoretical Nanoscience,2015年12(11):4383-4391 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, 550004, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, Hengyang, 421001, 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 two-neural networks with variable and unbounded delays. Using some analysis skills and Lyapunov method, a series of sufficient conditions for the existence and exponential stability of anti-periodic solutions to two-neural networks with variable and unbounded delays are presented. Our results are new and complement of some previously known ones.
期刊：
International Journal of Innovative Computing, Information and Control,2015年11(1):247-256 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;[Zhang, Qiming] College of Science, Hunan University of Technology, Wenhua Road, Zhuzhou, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, No. 28, West Xianning Road, Hengyang, China
通讯机构：
Guizhou Key Laboratory of Economics System, Simulation Guizhou University of Finance and Economics, Huaxi District, Guiyang, China
