Journal of East China Normal University(Natural Sc ›› 2005, Vol. 2005 ›› Issue (1): 9-15,3.

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The Structure of a Class of Polynomial Differential Systems of Degree 5 with a 25th order Singularity(Chinese)

SUN Ying1 , LI Xue-min2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China;2. Department of Mathematics, Shandong Normal University, Jinan 250014, China
  • Received:2003-12-01 Revised:2004-03-05 Online:2005-03-25 Published:2005-03-25
  • Contact: SUN Ying

Abstract: Using Poincaré transformation and Poincaré-Bendixson theorem,sufficient conditions for the existence, uniqueness and stability of the limit cycles for a kind of fifth order differential equation are obtained. It is proved that such a kind of systems has at most one limit cycle and the existence is accompanied by the stability.Furthermore, almost all possible global phase portraits, 64 altogether, are indicated.

Key words: finite singular point, infinite singular point, critical conditon, higher order singular point, finite singular point, infinite singular point, critical conditon

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