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Existence and Uniqueness of Limit Cycles for a Special System of DifferentialEquations on the Plane

机译：平面上一类特殊微分方程系统极限环的存在唯一性

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In the paper the authors discuss the limit cycle problem for the following systemof differential equations on the plane: dx/dt = -phi(y)(d(phi)/dy)H(x), dy/dt = q(x) + p(x)phi(y), where d(phi)/dy > 0 and both p(x) and q(x) are polynomials of degree two. Using Dulac's criterion necessary conditions for the existence of limit cycles are obtained. The existence of limit cycles is proved using the Andronov-Hopf theorem. After transforming the system to a Lienard system, the uniqueness of the limit cycle is proved by using a modification of a theorem by Zhang Zhifen. (Copyright (c) 1992 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)

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作者
Kooij, R. E.;
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年度 1992
页码 1-13
总页数 13
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Differential equations; Limit cycles; Saddle points; Existence theorems; Uniquenesstheorem; Polynomials;

机译：微分方程;极限环;鞍点;存在定理;唯一定理;多项式;

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3. Existence and Uniqueness of Limit Cycles in a Class of Planar Differential Systems [J] . Khalil I. T. Al-Dosary Journal of applied mathematics . 2011,第Pta11期

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7. Existence, uniqueness, and nonexistence of limit cycles for a class of quadratic systems in the plane [O] . Perko Lawrence M, Shih-Lung Shü 1984

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8. Existence and Uniqueness of Limit Cycles in Quadratic Systems of Class (III) subl=m=0 [R] . Kooij, R. E. 1990

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Existence and Uniqueness of Limit Cycles for a Special System of DifferentialEquations on the Plane

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