Bifurcations of small limit cycles in Lienard systems with cubic restoring terms

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Tian, Yun¹  Han, Maoan^1,2  Xu, Fangfang^3,4 

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[4] Qingdao Univ, Sch Automat, Qingdao 266071, Shandong, Peoples R China

关键词: Limit cycle;    Polynomial Lienard systems;    Hopf bifurcations;    Involutions;   

DOI  :  10.1016/j.jde.2019.02.018

来源: Elsevier

【 摘 要 】

In this paper, we study bifurcations of small-amplitude limit cycles of Lienard systems of the form (x) over dot = y - F(x), (y) over dot = -g(x), where g(x) is a cubic polynomial, and F(x) is a smooth or piecewise smooth polynomial of degree n. By using involutions, we obtain sharp upper bounds of the number of small-amplitude limit cycles produced around a singular point for some systems of this type. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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