期刊文献+
共找到306篇文章
< 1 2 16 >
每页显示 20 50 100
On the(1,3)Distributions of Limit Cycles of Plane Quadratic Systems
1
作者 蔺小林 党新益 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第5期471-483,共13页
In this paper, (a) we rerise Theorem 2 of Ref [1] omit the condition V_7>0 .(b) we discuss the relative positions of six curves M(s ̄2, r)=0, J( s ̄2, r)=0, L(s ̄2,r)=0, T(s ̄2,r)=0, Under the condition of the (1.3... In this paper, (a) we rerise Theorem 2 of Ref [1] omit the condition V_7>0 .(b) we discuss the relative positions of six curves M(s ̄2, r)=0, J( s ̄2, r)=0, L(s ̄2,r)=0, T(s ̄2,r)=0, Under the condition of the (1.3) distri-butions of limit cycles, we expand the variable regions of parameters ( s , r) and clearly. show them in figure, (c) we study the (1, 3) distributions of limit cycles of one kind quadratic systems with two singular points at the infinite: and (d) we give a generalmethod to discuss the ( 1 ,3) distibutions`of limit cycles of system (1.1) whatever there isone, two or three singular points at the infinite. 展开更多
关键词 quadratic system limit cycle
下载PDF
LIMIT CYCLE PROBLEM OF QUADRATIC SYSTEM OF TYPE ( Ⅲ )m=0, ( Ⅲ ) 被引量:2
2
作者 Ali. Elamin. M. Saeed Luo Dingjun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第4期431-440,共10页
To continue the discussion in (Ⅰ ) and ( Ⅱ ),and finish the study of the limit cycle problem for quadratic system ( Ⅲ )m=0 in this paper. Since there is at most one limit cycle that may be created from critic... To continue the discussion in (Ⅰ ) and ( Ⅱ ),and finish the study of the limit cycle problem for quadratic system ( Ⅲ )m=0 in this paper. Since there is at most one limit cycle that may be created from critical point O by Hopf bifurcation,the number of limit cycles depends on the different situations of separatrix cycle to be formed around O. If it is a homoclinic cycle passing through saddle S1 on 1 +ax-y = 0,which has the same stability with the limit cycle created by Hopf bifurcation,then the uniqueness of limit cycles in such cases can be proved. If it is a homoclinic cycle passing through saddle N on x= 0,which has the different stability from the limit cycle created by Hopf bifurcation,then it will be a case of two limit cycles. For the case when the separatrix cycle is a heteroclinic cycle passing through two saddles at infinity,the discussion of the paper shows that the number of limit cycles will change from one to two depending on the different values of parameters of system. 展开更多
关键词 quadratic system uniqueness of limit cycles homoclinic or heteroclinic cycle.
下载PDF
ON NUMBER OF LIMIT CYCLES FOR THE QUADRATIC SYSTEMS WITH A WEAK FOCUS AND A STRONG FOCUS 被引量:1
3
作者 Zhang Pingguang Zhao ShenqiDept.ofMath.ZhejiangUniv.,Hangzhou310027. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第2期127-132,共6页
It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system ha... It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution). 展开更多
关键词 quadratic differential system number of limit cycle weak focus strong focus.
下载PDF
NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM 被引量:1
4
作者 刘德明 《Acta Mathematica Scientia》 SCIE CSCD 1991年第1期65-71,共7页
In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We ... In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles. 展开更多
关键词 NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND uniqueness OF limit cycleS FOR A CLASS OF POLYNOMIAL system LIM
下载PDF
A METHOD PROVING THE UNIQUENESS OF THE LIMIT CYCLE OF THE QUADRATIC SYSTEM
5
作者 徐思林 朱豫根 《Annals of Differential Equations》 1996年第2期226-228,共3页
We transform the quadratic system into the special system of Type (Ⅲ)a=0' and hence a string sufficient conditions are established to ensure that the considered system has at most one limit cycle.
关键词 quadratic system limit cycle uniqueness.
原文传递
HOPF BIFURCATION AND UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF QUARTIC SYSTEM 被引量:2
6
作者 Zhan Qingyi Xie Xiangdong +1 位作者 Wu Chengqiang Qiu Shulin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第4期388-392,共5页
This paper studies a class of quartic system which is more general and realistic than the quartic accompanying system.x'=-y+ex+lx^2+mxy+ny^2,y'=x(1-Ay)(1+Cy^2),(*)where C 〉 0. Sufficient conditions are ... This paper studies a class of quartic system which is more general and realistic than the quartic accompanying system.x'=-y+ex+lx^2+mxy+ny^2,y'=x(1-Ay)(1+Cy^2),(*)where C 〉 0. Sufficient conditions are obtained for the uniqueness of limit cycle of system (*) and some more in-depth conclusion such as Hopf bifurcation. 展开更多
关键词 accompanying system bifurcation limit cycle uniqueness.
下载PDF
Uniqueness of Limit Cycle for the Quadratic Systems with Weak Saddle and Focus
7
作者 ShenQiZHAO PingGuangZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第4期647-652,共6页
It is proved that the quadratic system with a weak saddle has at most one limit cycle,and that if this system has a separatrix cycle passing through the weak saddle,then the stability of the separatrix cycle is contra... It is proved that the quadratic system with a weak saddle has at most one limit cycle,and that if this system has a separatrix cycle passing through the weak saddle,then the stability of the separatrix cycle is contrary to that of the singular point surrounded by it. 展开更多
关键词 quadratic system Weak saddle limit cycle Stability of separatrix cycle
原文传递
UNIQUENESS AND DISTRIBUTION OF LIMIT CYCLES FOR BOUNDED QUADRATIC SYSTEM
8
作者 宋矞 《Annals of Differential Equations》 2001年第4期352-362,共11页
In this paper, we first give a necessary and sufficient condition of a quadratic system with three finite critical points being bounded, and then, we use the methods and conclusions of [11] to provide some uniqueness ... In this paper, we first give a necessary and sufficient condition of a quadratic system with three finite critical points being bounded, and then, we use the methods and conclusions of [11] to provide some uniqueness theorems of limit cycles for bounded quadratic systems. As well, we prove that any bounded quadratic system can not have (2, 2)-distribution of limit cycles according to these uniqueness theorems. 展开更多
关键词 critical point Li■nard system uniqueness of limit cycles
原文传递
UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF QUARTIC SYSTEM ACCOMPANYING WITH QUADRATIC SYSTEM 被引量:1
9
作者 Zhan Qingyi(College of Computer and Information Science,Fujian Agriculture and Forestry University,Fuzhou 350002) Xie Xiangdong(Dept. of Math.,Ningde Teachers College,Ningde 352100,Fujian) Wu Chengqiang(College of Math. and Computer Science,Fuzhou University,Fuzhou 350002) 《Annals of Differential Equations》 2008年第2期239-245,共7页
In this paper,we consider a class of quartic system,which is more general and realistic than the quartic accompanying system. Consequently,we obtain sufficient conditions concerning the uniqueness of limit cycle as we... In this paper,we consider a class of quartic system,which is more general and realistic than the quartic accompanying system. Consequently,we obtain sufficient conditions concerning the uniqueness of limit cycle as well as some other in-depth conclusions. 展开更多
关键词 accompanying system limit cycle uniqueness
原文传递
Uniqueness of limit cycles of quadratic system (Ⅲ) _(m=0)
10
作者 ZHANG Xiang and YE Qin1.Department of Mathematics, Nanjing University, Nanjing 210093, China 2. Department of Applied Mathematics, Tongji University, Shanghai 200092, China 《Chinese Science Bulletin》 SCIE EI CAS 1997年第8期628-631,共4页
IN ref.[1]of § 20,Ye Yanqian has investigated the impossibility of(2,2)distribution of lim-it cycles of quadratic systems,where the footnote 1)on p.553 gives the following conjecture:The quadratic system(Ⅲ)&... IN ref.[1]of § 20,Ye Yanqian has investigated the impossibility of(2,2)distribution of lim-it cycles of quadratic systems,where the footnote 1)on p.553 gives the following conjecture:The quadratic system(Ⅲ)<sub>m=0</sub> 展开更多
关键词 quadratic system limit cycle uniqueness.
原文传递
THE UNIQUENESS OF LIMIT CYCLE OF QUADRATIC SYSTEM(Ⅱ)_(m=0)
11
作者 张平光 《Chinese Science Bulletin》 SCIE EI CAS 1990年第5期360-365,共6页
Without loss of generality, the quadratic system (Ⅱ)<sub>m=0</sub> can be assumed as follows:Generally, system (1) has four singular points, focus (node) 0(0,0), R(-1/a,y<sub>2</sub>... Without loss of generality, the quadratic system (Ⅱ)<sub>m=0</sub> can be assumed as follows:Generally, system (1) has four singular points, focus (node) 0(0,0), R(-1/a,y<sub>2</sub>), saddle N(0, 1), M(-1/a,y<sub>1</sub>), where y<sub>1, 2</sub>=[a±(a<sup>2</sup>-4(l-aδ))<sup>1/2</sup>]/2a. 展开更多
关键词 quadratic limit cycle uniqueness.
原文传递
Existence of Limit Cycles for a Cubic Kolmogorov System with a Hyperbolic Solution 被引量:4
12
作者 沈伯骞 刘德明 《Northeastern Mathematical Journal》 CSCD 2000年第1期91-95,共5页
This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system ma... This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles. 展开更多
关键词 cubic kolmogorov system central quadratic curve limit cycle
下载PDF
The Quadratic System Having a Parabola as Its Integral Curve Has at Most One Limit Cycle
13
作者 谢向东 蔡燧林 《Chinese Science Bulletin》 SCIE EI CAS 1994年第4期265-267,共3页
In this note, we prove that the quadratic system having a parabola as its integralcurve has at most one limit cycle, and therefore the quadratic system havingquadratic curve as its integral curve has at most one limjt... In this note, we prove that the quadratic system having a parabola as its integralcurve has at most one limit cycle, and therefore the quadratic system havingquadratic curve as its integral curve has at most one limjt cycle. Considering Ref.[1], we have solved completely the problem of the bifurcations of limit cycle forsystem (1). 展开更多
关键词 quadratic system integral curve limit cycle.
原文传递
STUDY OF NON-EXISTENCE OF LIMIT CYCLE AROUND A WEAK FOCUS OF ORDER TWO OR THREE FOR QUADRATIC SYSTEMS
14
作者 张平光 《Chinese Science Bulletin》 SCIE EI CAS 1990年第14期1156-1161,共6页
On the basis of[2—4], we only need to consider the case of n≠0. Without loss of generality, we can assume n=1, a】0. Hence the system(1)<sub>n,0</sub> can be written as(1)<sub>1,0</sub>
关键词 quadratic system limit cycle non-existence.
原文传递
ON THE NON-EXISTENCE OF LIMIT CYCLES OF CERTAIN QUADRATIC SYSTEMS
15
作者 YE WEIYIN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1998年第3期359-368,共10页
In §1 and §3, two conjectures mentioned by Ye Yanqian are studied. In §2, by use of elementary methods the author proves some non-existence theorems of limit cycles (LC, for abbreviation) for quadrat... In §1 and §3, two conjectures mentioned by Ye Yanqian are studied. In §2, by use of elementary methods the author proves some non-existence theorems of limit cycles (LC, for abbreviation) for quadratic differential systems obtained recently by H.Giacomini, J. Llibre and M. Viano. 展开更多
关键词 quadratic differential system limit cycle
全文增补中
Limit cycle problem for quadratic differential system x = -y + lx^2 + mxy, y =x(1 +ax +by)
16
作者 陆炳新 罗定军 《Journal of Southeast University(English Edition)》 EI CAS 2004年第4期517-520,共4页
The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equa... The maximal number of limit cycles for a particular type Ⅲ system x = -y + lx2 + mxy, y =x(1 + ax + by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003,19(3):397-401) are corrected. By translating the system to be considered into the Lienard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue's paper mentioned above. 展开更多
关键词 quadratic differential system limit cycle weak focus
下载PDF
BIFURCATION OF LIMIT CYCLES FOR THE QUADRATIC DIFFERENTIAL SYSTEM (Ⅲ)l = n = 0
17
作者 张祥 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1999年第4期368-373,共6页
In this paper we will prove that limit cycles for the quadratic differential system (Ⅲ)l=n=o in Chinese classification are concentratedly distributed, and that the maximum number of limit cycles around O(0,0) is at l... In this paper we will prove that limit cycles for the quadratic differential system (Ⅲ)l=n=o in Chinese classification are concentratedly distributed, and that the maximum number of limit cycles around O(0,0) is at least two. 展开更多
关键词 quadratic system limit cycle BIFURCATION
全文增补中
THE UNIQUENESS OF LIMIT CYCLE AND THE STRUCTURE OF CRITICAL POINT AT INFINITY FOR A CLASS OF CUBIC SYSTEM 被引量:11
18
作者 Xie Xiangdong Chen Fengde 《Annals of Differential Equations》 2005年第3期474-479,共6页
A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. Th... A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained. 展开更多
关键词 cubic system accompany system limit cycle uniqueness
原文传递
ON A CONJECTURE CONCERNING THE NON-EXISTENCE OF LIMIT CYCLES FOR QUADRATIC DIFFERENTIAL SYSTEMS 被引量:6
19
作者 叶彦谦 《Annals of Differential Equations》 2000年第4期391-400,共10页
A conjecture on the non-existence of limit cycles for the quadratic differential system (1) under conditions (2) and iv) of (3) is discussed; interesting phenomena are revealed.
关键词 limit cycle quadratic differential system DIVERGENCE
原文传递
THE UNIQUENESS OF LIMIT CYCLE OF THE POLYNOMIAL LIENARD SYSTEM OF DEGREE 4 被引量:1
20
作者 陆炳新 《Annals of Differential Equations》 2004年第4期379-384,共6页
In this paper, the uniqueness of limit cycle of a special polynomial Lienard system is discussed and some results under certain conditions are given.
关键词 uniqueness limit cycle Lienard system
原文传递
上一页 1 2 16 下一页 到第
使用帮助 返回顶部