SIXTEEN LARGE-AMPLITUDE LIMIT CYCLES IN A SEPTIC SYSTEM | Zendy

Lina Zhang | Zendy; Feng Li | Zendy; Ahmed Alsaedi | Zendy

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SIXTEEN LARGE-AMPLITUDE LIMIT CYCLES IN A SEPTIC SYSTEM

Author(s) -

Lina Zhang,

Feng Li,

Ahmed Alsaedi

Publication year - 2018

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 - 10.11948/2018.1821

Subject(s) - infinity , limit (mathematics) , mathematics , mathematical analysis , amplitude , limit cycle , bifurcation , polynomial , singular point of a curve , infinite period bifurcation , differential (mechanical device) , hopf bifurcation , physics , nonlinear system , quantum mechanics , thermodynamics

In this paper, bifurcation of limit cycles from the infinity of a twodimensional septic polynomial differential system is investigated. Sufficient and necessary conditions for the infinity to be a center are derived and the fact that there exist 16 large amplitude limit cycles bifurcated from the infinity is proved as well. The study relays on making use of a recursive formula for computing the singular point quantities of the infinity. As far as we know, this is the first example of a septic system with 16 limit cycles bifurcated from the infinity.

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