NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

数学物理学报(英文版) ›› 1991, Vol. 11 ›› Issue (1): 65-71.

NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

刘德明

Dept. of Math., Shenyang Teacher's College, Shenyang, China

收稿日期:1988-04-02 出版日期:1991-03-25 发布日期:1991-03-25

NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

Liu Deming

Dept. of Math., Shenyang Teacher's College, Shenyang, China

Received:1988-04-02 Online:1991-03-25 Published:1991-03-25

摘要/Abstract

摘要： In this paper, we discuss the limit cycles of the system
dx/dt=y·[1+(A(x)]dy/dt=(-x+δy+a₁x²+a₂xy+a₅x²y)[1+B(x)] (1)where A(x)=Σ_i=1ⁿa_ixⁱ, B(x)=Σ_j=1^m(B_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.

刘德明. NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM[J]. 数学物理学报(英文版), 1991, 11(1): 65-71.

Liu Deming. NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM[J]. Acta mathematica scientia,Series B, 1991, 11(1): 65-71.

NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

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