检索结果-南通市图书馆

limit cycles AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2008年第4期28卷 865-869页

作者：刘振海 E.Sáez I.Szántó Department of Mathematics Changsha University of Sciences and Techndogy Departamento de Matemática Universidad Tcnica Federico Santa MariaCasilla 110-VValparaisoChile

In this article,the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant *** this class of second-order differential systems,it is shown that for certain values of the parameters the invariant parabola coexists with a *** other values it can coexist with one,two or three small amplitude limit cycles which are constructed by Hopf *** result gives an answer for the question given in[4],about the existence of limit cycles for such class of system.

关键词： Kukles system limit cycles invariant algebraic curves

limit cycles AND CENTER-FOCUS OF NONLINEAR SYSTEMS

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 1998年第4期13卷 385-390页

作者： WANGXIANGRONG HANMAOAN DepartmentofAppliedMathematlcs ShandongInstituteofMiningandTechnologyTaian271019. DepartmentofAppliedMathematics ShanghaiJiaotongUniversityShanghai200030.

Abstract The authors consider the nonlinear systems [AKx·D6]=h(y)-F(x),=-g(x) in which g(x) may be not differentiable and the system can be nonsymmetric. Some conditions which ensure that there exists an infinite number of limit cycles are obtained. A problem about center focus put forward by R. Conti has been answered.

关键词： nonlinear systems limit cycles center-focus

Four limit cycles for a Rock-Scissor-Paper Game Between Bacteriocin Producing Bacteria

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2023年第5期36卷 2225-2233页

作者： MA Sibi HU Mingzhi LU Zhengyi School of Mathematical Sciences Sichuan Normal UniversityChengdu 610068China

In this paper,four limit cycles are constructed for a concrete 3D model of rock-scissorpaper(RSP)game between bacteriocin producing *** gives not only an affirmative answer to the conjecture of the existence of three ... 详细信息

关键词： Bacteriocin limit cycles rock-scissor-paper game

Z_2-Equivariant Cubic System Which Yields 13 limit cycles

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2014年第3期30卷 781-800页

作者： Yi-rong LIU Ji-bin LI School of Mathematics Central South University Department of Mathematics Zhejiang Normal University School of Science Kunming University of Science and Technology

For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small Z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.

关键词： planar dynamical system limit cycles bifurcations Lyapnov constant weak focus

Bifurcations of limit cycles in A Perturbed Quintic Hamiltonian System with Six Double Homoclinic Loops

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2008年第2期24卷 313-328页

作者： Yong-xi Gao Yu-hai Wu Li-xin Tian Department of Mathematics Jiang Su University Zhenjiang 212013 China

This paper concerns with the number and distributions of limit cycles of a quintic subject to a seven-degree perturbation. With the aid of numeric integral computation provided by Mathematica 4.1, at least 45 limit cycles are found in the above system by applying the method of double homoclinic loops bifurcation, Hopf bifurcation and qualitative analysis. The four configurations of 45 limit cycles of the system are also shown. The results obtained are useful to the study of the weakened 16th Hilbert Problem.

关键词： limit cycles the Hilbert's 16th problem the double homoclinic loops stability Poincare-Bendixsontheorem

The Same Distribution of limit cycles in a Hamiltonian System with Nine Seven-order Perturbed Terms

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2008年第1期24卷 167-176页

作者： Tao Jiang Zhi-yan Yang School of Information Beijing Wuzi University Beijing 101149 China

Using qualitative analysis and numerical simulation, we investigate the number and distribution of limit cycles for a cubic Hamiltonian system with nine different seven-order perturbed terms. It is showed that these perturbed systems have the same distribution of limit cycles. Furthermore, these systems have 13, 11 and 9 limit cycles for some parameters, respectively. The accurate positions of the 13, 11 and 9 limit cycles are obtained by numerical exploration, respectively. Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles. This is useful for studying limit cycles of perturbed systems.

关键词： limit cycles bifurcation

Center, limit cycles and Isochronous Center of a Z_4-equivariant Quintic System

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2010年第6期26卷 1183-1196页

作者： Chao Xiong DU Hei Long MI Yi Rong LIU Department of Hu'nan Shaoyang University Shaoyang 422000 P. R. China and School of Mathematics Central South University Changsha 410083 P. R. China Department of Information Science Hu'nan Commercial University Changsha 410083 P. R. China School of Mathematics Central South University Changsha 410083 P. R. China

In this paper, we study the limit cycles bifurcations of four fine focuses in Z4-equivariant vector fields and the problems that its four singular points can be centers and isochronous centers at the same time. By computing the Liapunov constants and periodic constants carefully, we show that for a certain Z4-equivariant quintic systems, there are four fine focuses of five order and five limit cycles can bifurcate from each, we also find conditions of center and isochronous center for this system. The process of proof is algebraic and symbolic by using common computer algebra soft such as Mathematica, the expressions after being simplified in this paper are simple relatively. Moreover, what is worth mentioning is that the result of 20 small limit cycles bifurcating from several fine focuses is good for Z4-equivariant quintic system and the results where multiple singular points become isochronous centers at the same time are less in published references.

关键词： Z4-equivariant focal value center limit cycles isochronous center

Bifurcations of limit cycles in a Z_4-Equivariant Quintic Planar Vector Field

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2010年第4期26卷 779-798页

作者： Yu Hai WU Xue Di WANG Li Xin TIAN Department of Mathematics Jiangsu University Zhenjiang 212013 P. R. China

In this paper, a Z4-equivariant quintic planar vector field is studied. The Hopf bifurcation method and polycycle bifurcation method are combined to study the limit cycles bifurcated from the compounded cycle with 4 hyperbolic saddle points. It is found that this special quintic planar polynomial system has at least four large limit cycles which surround all singular points. By applying the double homoclinic loops bifurcation method and Hopf bifurcation method, we conclude that 28 limit cycles with two different configurations exist in this special planar polynomial system. The results acquired in this paper are useful for studying the weakened 16th Hilbert＇s Problem.

关键词： compounded cycle double homoclinic loops stability bifurcation limit cycles distribution of limit cycles

On the limit cycles of a quintic planar vector field

在线全文

学校读者我要写书评

暂无评论

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