ON THE LIMIT CYCLES OF A KIND OF LI&#201;NARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS | Zendy

Junmin Yang | Zendy

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ON THE LIMIT CYCLES OF A KIND OF LIÉNARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS

Author(s) -

Junmin Yang

Publication year - 2012

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2012024

Subject(s) - nilpotent , center (category theory) , physics , limit (mathematics) , mathematics , combinatorics , mathematical analysis , crystallography , chemistry

In this paper, we study the limit cycles of a kind of Li e nar d systemwith a nilpotent center under perturbations. Let L(m; n) denote the numberof limit cycles of this Li e nard system ẋ = y- ɛ F(x) ; ẏ =-g (x) near theorigin, where m = deg g; n = deg F. We o btain some results of L(m; n) for m = 4; 2 n ≤ 20, m = 5, 2 ≤ 10, m = 6, 2 ≤ n ≤ 5, m = 7, 2 ≤ n ≤ 4, where some results are new.

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