On the Dynamics of the Unified Chaotic System between Lorenz and Chen Systems

Jaume Llibre, Ana Rodrigues

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


© 2015 World Scientific Publishing Company. A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole R3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.
Original languageEnglish
Article number1550122
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number9
Publication statusPublished - 8 Aug 2015


  • Chen system
  • Hopf bifurcation
  • Lorenz system
  • Poincaré compactification
  • invariant algebraic surface
  • unified chaotic system


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