A Chaotic System with a Single Unstable Node

J. C. Sprotta, Sajad Jafarib, Viet-Thanh Phamc, Zahra Sadat Hosseinib

a Department of Physics, University of Wisconsin, Madison, WI 53706, USA
b Biomedical Engineering Department, Amikabir University of Technology, Tehran 15875-4413, Iran
c School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam

Received 19 October 2014
Received in revised form 27 April 2015
Accepted 16 June 2015
Available online 19 June 2015
Communicated by A.P. Fordy

This paper describes an unusual example of a three-dimensional dissipative chaotic flow with quadratic nonlinearities in which the only equilibrium is an unstable node. The region of parameter space with bounded solutions is relatively small as is the basin of attraction, which accounts for the difficulty of its discovery. Furthermore, for some values of the parameters, the system has an attracting torus, which is uncommon in three-dimensional systems, and this torus can coexist with a strange attractor or with a limit cycle. The limit cycle and strange attractor exhibit symmetry breaking and attractor merging. All the attractors appear to be hidden in that they cannot be found by starting with initial conditions in the vicinity of the equilibrium, and thus they represent a new type of hidden attractor with important and and potentially problematic engineering consequences.

Ref: J. C. Sprott, S. Jafari, V-T. Pham, and Z. S. Hosseini, Phys. Lett. A 379, 2030-2036 (2015)

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