How to obtain extreme multistability in coupled dynamical systems

C. R. Hens, R. Banerjee, U. Feudel, S. K. Dana

Research output: Contribution to journalArticlepeer-review

94 Scopus citations


We present a method for designing an appropriate coupling scheme for two dynamical systems in order to realize extreme multistability. We achieve the coexistence of infinitely many attractors for a given set of parameters by using the concept of partial synchronization based on Lyapunov function stability. We show that the method is very general and allows a great flexibility in choosing the coupling. Furthermore, we demonstrate its applicability in different models, such as the Rössler system and a chemical oscillator. Finally we show that extreme multistability is robust with respect to parameter mismatch and, hence, a very general phenomenon in coupled systems.

Original languageEnglish
Article number035202
JournalPhysical Review E
Issue number3
StatePublished - 13 Mar 2012
Externally publishedYes


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