Strange Attractors with Various Equilibrium Types

J. C. Sprott
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA

Received: 26 January 2015 / Received in final form 20 May 2015 Published online 27 July 2015


Of the eight types of hyperbolic equilibrium points in three-dimensional flows, one is overwhelmingly dominant in dissipative chaotic systems. This paper shows examples of chaotic systems for each of the eight types as well as one without any equilibrium and two that are nonhyperbolic. The systems are a generalized form of the Nose-Hoover oscillator with a single equilibrium point. Six of the eleven cases have hidden attractors and six of them exhibit multistability for the chosen parameters.

Ref: J. C. Sprott, The European Physical Journal Special Topics 224 1409-1419 (2015)

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