A classical technique for analyzing dynamical systems is due to Poincaré. It replaces the flow of an nth-order continuous-time system with an (n − 1)th-order discrete-time system called the Poincaré map. The definition of the Poincaré map ensures that its limit sets correspond to limit sets of the underlying flow. The Poincaré map’s usefulness lies in the reduction of order and the fact that it bridges the gap between continuous- and discrete-time systems.


Autonomous System Closed Orbit Chaotic Orbit Autonomous Case Dimensional Hyperplane 
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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Thomas S. Parker
    • 1
  • Leon O. Chua
    • 2
  1. 1.Hewlett PackardSanta RosaUSA
  2. 2.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

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