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QUADRATIC SYSTEMS WITH A 3RD-ORDER (OR 2ND-ORDER) weak focus

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Annals of Differential Equations 2001年第3期17卷 287-294页

作者：张平光 Dept. of Math. Zhejiang University Hangzhou 310027

In this paper, we prove that a planar quadratic systems with a 3rd-order weak focus has at most one limit cycle, and a planar quadratic system with a 2nd-order weak focus has at most two limit cycles.

关键词： quadratic system weak focus limit cycle uniqueness

Z_2-Equivariant Cubic System Which Yields 13 Limit Cycles

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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

NOTE ON “BIFURCATION OF A PREDATOR-PREY MODEL WITH UNDERCROWDING EFFECT”

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Applied Mathematics(A Journal of Chinese Universities) 2003年第3期18卷 370-372,F003页

作者： Yang MingchaoDept. of Math., Zhejiang Univ., Hangzhou 310027, China. Dept. of Math. Zhejiang Univ. Hangzhou China

Inexistence and existence of limit cycles in a predator-prey model with undercrowding effect are *** number of limit cycles obtained by Zheng Weiwei in 2000 is corrected.

关键词： predator-prey system weak focus limit cycle

THE MAXIMAL NUMBER OF LIMIT CYCLES FOR QUADRATIC DIFFERENTIAL SYSTEM  = -y + lx^2 + xy,  = x(l + ax + by)

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Annals of Differential Equations 2003年第3期19卷 397-401页

作者：索明霞岳锡亭 Dept. of Math. Changchun Teacher College Changchun 130032 School of Basic Sciences Changchun University of Technology Changchun 180012

In this paper, we investigate the maximal number of limit cycles surrounding a first order weak focus for the quadratic differential system. And proved such a system has at most two limit cycles under some certain con... 详细信息

关键词： limit cycles weak focus

Limit cycle problem for quadratic differential system x = -y + lx^2 + mxy, y =x(1 +ax +by)

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Journal of Southeast University(English Edition) 2004年第4期20卷 517-520页

作者：陆炳新罗定军南京师范大学数学与计算机科学学院南京210097

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.

关键词： quadratic differential system limit cycle weak focus