Why are chaotic attractors rare in multistable systems?

U Feudel, C Grebogi

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)


We show that chaotic attractors are rarely found in multistable dissipative systems close to the conservative limit. As we approach this limit, the parameter intervals for the existence of chaotic attractors as well as the volume of their basins of attraction in a bounded region of the state space shrink very rapidly. An important role in the disappearance of these attractors is played by particular points in parameter space, namely, the double crises accompanied by a basin boundary metamorphosis. Scaling relations between successive double crises are presented. Furthermore, along this path of double crises, we obtain scaling laws for the disappearance of chaotic attractors and their basins of attraction.

Original languageEnglish
Article number134102
Number of pages4
JournalPhysical Review Letters
Issue number13
Publication statusPublished - 26 Sept 2003


  • multiple steady-states
  • dissipative systems
  • periodic attractors
  • double crises
  • metamorphoses
  • transition
  • reactors
  • array


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