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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
Citation: 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

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

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  • Received Date: December 23, 2018
  • Available Online: March 21, 2021
  • The equilibrium points of a class of plane cubic polynomial systems =-y+αx2-αy2+βx3-3βxy2, =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.
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