Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1698–1708 | Cite as

Computation of Invariant Curves and Identifying the Type of Critical Point

  • Junhai Zhi
  • Yufu ChenEmail author


This paper considers two dimensional systems which have purely imaginary eigenvalues. In order to obtain more propositions of invariant curves, the authors transform the real systems into complex differential systems by using a suitable linear transformation. The authors also propose an algorithm to compute exponential factors. An improved method of constructing integrating factor by using all invariant curves is presented and can be used in determining the type of the equilibrium points.


Complex differential system equilibrium point exponential factor invariant curve 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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