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Periodic solutions and flip bifurcation in a linear impulsive system

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Chinese Physics B 2008年第11期17卷 4114-4122页

作者：蒋贵荣杨启贵 school of Mathematical sciences South China University of Technology school of mathematics and computing science Guilin University of Electronic Technology

In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.

关键词： linear impulsive equation periodic solution flip bifurcation

Bifurcation control and chaos in a linear impulsive system

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Chinese Physics B 2009年第12期18卷 5235-5241页

作者：蒋贵荣胥布工杨启贵 school of Mathematical sciences South China University of Technology school of mathematics and computing science Guilin University of Electronic Technology College of Automation science and Engineering South China University of Technology

Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto＇s definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.

关键词： periodic solution bifurcation control chaos controller

The Decision of Prime and Primary Ideal

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Acta Mathematicae Applicatae Sinica 2011年第4期27卷 595-600页

作者： Jin-wang LIU Dong-mei LI school of mathematics and computing sciences Hunan University of Science and Technology Xiangtan 411201 China school of Mathematical science and computing technology Central South University Changsha 410083 China

We give more efficient criteria to characterise prime ideal or primary ideal. Further, we obtain the necessary and sufficient conditions that an ideal is prime or primary in real field from the Grobner bases directly.

关键词： Grobner basis prime ideal orimarv ideal

Mean-square exponential stability of stochastic Volterra systems in infinite dimensions

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science China(Information sciences) 2024年第10期67卷 298-314页

作者： Lin FU Shiguo PENG Feiqi DENG Quanxin ZHU school of Automation Guangdong University of Technology school of Automation science and Engineering South China University of Technology Key Laboratory of computing and Stochastic mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal University

Over the past decade, the study of stability theory in integro-differential systems has grown significantly owing to their relevance in solving physical and engineering problems, such as viscoelasticity and thermo-viscoelasticity in materials with memory properties. This paper concentrates on a class of infinite-dimensional stochastic integro-differential systems. We establish the well-posedness of the system and identify mild solutions to the system and an abstract stochastic Cauchy problem. This identification is identified by employing a semigroup approach combined with Yosida approximation. We derive sufficient conditions that ensure the mean-square exponential stability of mild solutions to the system boils down to the boundedness of a certain function and a norm estimate for the stochastic part. These conditions are implemented through the semigroup approach and the composition operator method. Illustrative examples are provided and the obtained theoretical results are validated by numerical simulations.

关键词： stochastic integro-differential equations mean-square exponential stability stochastic distributed parameter systems Hardy space composition operators

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MARKOV CHAIN-BASED ANALYSIS OF THE DEGREE DISTRIBUTION FOR A GROWING NETWORK

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Acta Mathematica Scientia 2011年第1期31卷 221-228页

作者：候振挺童金英史定华 school of Mathematical science and computing technology Central South University school of sciences Donghua University Department of mathematics Shanghai University

In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.

关键词： Growing networks preferential attachment power law

Strong convergence results for hemivariational inequalities

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science China mathematics 2006年第7期49卷 893-901页

作者： LIU Zhenhai ZOU Jiezhong Department of mathematics Changsha University of Science and Technology Changsha 410076 China school of Mathematical science and computing technology Central South University Changsha 410075 China School of Mathematical Science and Computing Technology Central South University Changsha 410075 China

The purpose of this paper is to study a regularization method of solutions of ill-posed problems involving hemivariational inequalities in Banach spaces. Under the assumption that the hemivariational inequality is solvable, a strongly convergent approximation procedure is designed by means of the so-called Browder-Tikhonov regularization method. Our results generalize and extend the previously known theorems.

关键词： hemivariational inequalities, Clarke subdifferential, regularization, strong convergence.

L_(p,q)-norm estimates associated with Burkholder’s inequalities

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science China mathematics 2011年第12期54卷 2713-2721页

作者： jIAO Yong school of mathematics science and computing technology Central South University Changsha 410075 China

We prove Burkholder's inequalities in the frame of Lorentz spaces Lp,q(Ω), 1 < p < ∞, 1 < q < ∞. As application, we obtain the Lp,q-norm estimates on Rosenthal's inequalities. These estimates generalize the classic... 详细信息

关键词： Lorentz spaces martingales Burkholder's inequalities Rosenthal's inequalities

The k-point Exponent Set of Primitive Digraphs with Girth 2

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 573-582页

作者： She-xi Chen Wei-jun Liu Jin-wang Liu school of mathematics and Computational science Hunan University of Science and Technology Xiangtan411201 China school of mathematics sciences and computing technology Central South University Changsha 410075 China

Let D = （V, E） be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD（v）, is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD（V1） ≤ exPD（V2） …≤ exPD（Vn）. Then exPD（Vk） is called the k- point exponent of D and is denoted by exPD （k）, 1≤ k ≤ n. In this paper we define e（n, k）：= max{expD （k）｜ D ∈ PD（n, 2）} and E（n, k）：= {exPD（k）｜ D ∈ PD（n, 2）}, where PD（n, 2） is the set of all primitive digraphs of order n with girth 2. We completely determine e（n, k） and E（n, k） for all n, k with n ≥ 3 and 1 ≤ k ≤ n.

关键词： Primitive digraph k-point exponent exponent set

Equations of Langmuir turbulence and Zakharov equations:smoothness and approximation

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Applied mathematics and Mechanics(English Edition) 2012年第8期33卷 1079-1092页

作者：游淑军郭柏灵宁效琦 school of Mathematical science and computing technology Central South University Department of mathematics Huaihua University Institute of Applied Physics and Computational mathematics

A family of systems parameterized by H 〉 0, which describes the Langmuir turbulence, is considered. The asymptotic behavior of the solutions （E^H, nH） when H goes to zero is studied. The results of convergence of ... 详细信息

关键词： Zakharov equation equation of Langmuir turbulence approximation