On the Darboux integrability of the Hindmarsh–Rose burster

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review


© 2018, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature. We study the Hindmarsh–Rose burster which can be described by the differential system x˙ = y− x3+ bx2+ I− z, y˙ = 1 − 5 x2− y, z˙ = μ(s(x− x0) − z) , where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
Original languageEnglish
Pages (from-to)947-958
JournalActa Mathematica Sinica, English Series
Issue number6
Publication statusPublished - 1 Jun 2018


  • Darboux first integrals
  • Darboux polynomials
  • Hindmarsh–Rose burster
  • Polynomial integrability
  • exponential factors
  • invariant algebraic surfaces
  • rational integrability


Dive into the research topics of 'On the Darboux integrability of the Hindmarsh–Rose burster'. Together they form a unique fingerprint.

Cite this