An Equilibrium Point Analysis of a Class of Planar Cubic Polynomial Systems

LONG Neng; LIANG Haihua

doi:10.6054/j.jscnun.2019107

Journal of South China Normal University (Natural Science Edition) > 2019 > 51(6): 98-102. > DOI: 10.6054/j.jscnun.2019107

LONG Neng, LIANG Haihua. An Equilibrium Point Analysis of a Class of Planar Cubic Polynomial Systems[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(6): 98-102. DOI: 10.6054/j.jscnun.2019107

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An Equilibrium Point Analysis of a Class of Planar Cubic Polynomial Systems

LONG Neng,
LIANG Haihua^,

School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China

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Received Date: December 23, 2018
Available Online: March 21, 2021

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Abstract

Abstract

The equilibrium points of a class of plane cubic polynomial systems ẋ=-y+αx²-αy²+βx³-3βxy², ẏ=x-2αxy+3βx²y-βy³ are discussed. It is proved that when |α-1|≪0, |β-1|≪0, there are four infinite equilibrium points and all of them are saddle points, and there are three finite equilibrium points and all of them are focal points. The position, order and stability of the three focal points are given.
- cubic systems,
- infinity,
- equilibrium point,
- Poincaré transformation

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