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On Stability Discrimination of Limit Cycles for Piecewise Smooth Systems

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1785-1803页

作者： mao an han Xia Yu ZHOU School of Mathematical Sciences Zhejiang Normal UniversityJinhua321004P.R.China

This paper is concerned with the problem of stability discrimination of limit cycles for piecewise smooth *** first establish the Poincaré map near a periodic orbit,and deduce the first order derivative of the map for general piecewise smooth systems on the ***,we obtain a sufficient condition for determining the stability of limit cycles for these systems.

关键词： Piecewise smooth system limit cycle stability

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On the Number of Limit Cycles of a Z_4-equivariant Quintic Near-Hamiltonian System

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Acta Mathematica Sinica,English Series 2015年第11期31卷 1805-1824页

作者： Xian Bo SUN mao an han Department of Applied Mathematics Guangxi University of Finance and Economics The Institute of Mathematics Shanghai Normal University

In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.

关键词： Limit cycle near-Hamiltonian system heteroclinic loop Za-equivariance Hopf bifurca-tion

On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z_3 Invariant Quintic Perturbations

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Acta Mathematica Sinica,English Series 2007年第5期23卷 869-878页

作者： Yu Hal WU mao an han Department of Mathematics Jiang Su University Zhenjiang 212013 P. R. China Department of Mathematics Shanghai Normal University Shanghai 200234 P. R. China

A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered. By applying the qualitative method of differential equations and the numeric computing method, the Hopf bifurcation, homoclinic loop bifurcation and heteroclinic loop bifurcation of the above perturbed system are studied. It is found that the above system has at least 12 limit cycles and the distributions of limit cycles are also given.

关键词： homoclinic loop bifurcation heteroclinic loop bifurcation Hopf bifurcation stability limit cycles

Environmental influence of Wuhan urban agglomeration development and strategies of environmental protection

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Journal of Environmental Sciences 2006年第3期18卷 616-623页

作者： GAO Qun LIU Ying-tao mao han-ying Institute of Geographic Sciences and Natural Resources Research Chinese Academy of Sciences Beijing 100101 China Chinese Academy of Agricultural Sciences Beijing 100081 China

In Wuhan urban agglomeration （WUA）, the population growth and concentration, the industrial development and urban sprawl have been affecting the environment ftmdamentally. Comparing with Yangtze delta metropolitan region, the level of urbanization and industrialization of WUA has lagged behind for about 10 years; but the problems in environmental protection and rehabilitation are commonly serious. In the future, WUA should avoid unnecessary mistakes and seek a win-win strategy for economy and environment in its large-scale development stage. Based on the analysis of the changing of main environmental pollutants and the coupled curves in past decades, the paper discussed the important links among the urban environmental pollutions, industry growth and urban sprawl in WUA. It is concluded that the integration of economic and environmental policies in urban development is more required and significant at the large urban agglomeration region. Four proactive and long-term strategies need to be adopted to provide prior guidance and better protection for the development of WUA.

关键词： environmental problem urban development Wuhan urban agglomeration strategies

Progress of energy system with chemical-looping combustion

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Chinese Science Bulletin 2009年第6期54卷 906-919页

作者： JIN HongGuang HONG Hui han mao Institute of Engineering Thermophysics Chinese Academy of Sciences Box 2706 Beijing 100190 China

Chemical-looping combustion with zero energy penalty of CO2 separation is a significant breakthrough in resolving energy and environment problems for power generation systems. This paper summarizes the research on energy systems with chemical-looping combustion conducted in recent years, discloses the underlying mechanism of energy release of chemical-looping combustion, describes the trends of the key technology development, and presents the proposed chemical-looping combustion thermal cycles. This paper may provide a new direction to the synthesis of the next-generation energy system compatible with environment.

关键词：循环燃烧能源系统化学环境问题发电系统能量释放系统兼容 CO2

Periodic Solutions of a Discrete Time Predator-Prey System

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Acta Mathematicae Applicatae Sinica 2006年第3期22卷 397-404页

作者： Yong-li Song mao-an han Department of Applied Mathematics Tongji University Shanghai 200092 China Department of Mathematics Shanghai Normal University Shanghai 200234 China

In this paper, we discuss a discrete predator-prey system with a non-monotonic functional response, which models the dynamics of the prey and the predator having non-overlapping generations. By using the coincidence d... 详细信息

关键词： Predator-prey system discrete time periodic solution coincidence degree

Investigation of stressful life events in patients with systemic sclerosis

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Journal of Zhejiang University-Science B(Biomedicine & Biotechnology) 2008年第11期9卷 853-856页

作者： Yue CHEN Ji-zhong HUANG Yu QIANG Jin WANG mao-mao han Department of Geriatrics the First Affiliated Hospital School of Medicine Zhejiang University Hangzhou 310009 China Department of Surgery Hangzhou Tongji Hospital Hangzhou 310012 China

Objective: To assess the occurrence of stressful life events in the year before the initiation of systemic sclerosis. Methods: A consecutive series of 40 patients with systemic sclerosis (mean age (56.3±11.9) years, mean disease duration (4.3±3.1) years; 32 females and 8 males), including 28 with diffuse cutaneous scleroderma and 12 with limited cutaneous scleroderma, were evaluated. A control group of 40 healthy subjects free of systemic sclerosis also was included. Socioeconomic status was inves- tigated and Paykel's interview for recent life events (a semi-structured research interview covering 64 life events) was conducted. Results: Patients with systemic sclerosis showed higher percentages of lower education (72.5%) and working class (82.5%), and reported more stressful life events (Phan in the control. These results are in accordance with a multifactorial model of pathogenesis in systemic sclerosis. Conclusion: We reported a strong relationship between stressful life events and the initiation of systemic sclerosis. Our findings are consistent with current understanding of the extensive links of behavioral responses to stress with neurophysiological and biochemical processes.

关键词： Systemic sclerosis (SSc) Life events Stress Pathogenesis

Bifurcation of limit cycles near equivariant compound cycles

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Science China Mathematics 2007年第4期50卷 503-514页

作者： mao-an han Tong-hua ZhanG Hong ZANG Department of Mathematics Shanghai Normal UniversityShanghai 200234China

In this paper we study some equivariant systems on the plane. We first give some criteria for the outer or inner stability of compound cycles of these systems. Then we investigate the number of limit cycles which appear near a compound cycle of a Hamiltonian equivariant system under equivariant perturbations. In the last part of the paper we present an application of our general theory to show that a Z3 equivariant system can have 13 limit cycles.

关键词： equivariant system stability bifurcation limit cycle 34C05 34G10 58F11

On the limit cycles of a quintic planar vector field

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Science China Mathematics 2007年第7期50卷 925-940页

作者： Yu-hai WU Li-xin TIAN mao-an han Department of Mathematics Jiangsu UniversityZhenjiang 212013China Department of Mathematics Shanghai Normal UniversityShanghai 200234China

This paper concerns the number and distributions of limit cycles in a Z 2-equivariant quintic planar vector field. 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation. It can be concluded that H(5) ? 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to study the weakened 16th Hilbert problem.

关键词： double homoclinic loop Melnikov function stability bifurcation limit cycles configuration 34C07 34C23 34C37 37G15