ABOUT UNIVERSAL BASINS OF ATTRACTION IN
HIGH-DIMENSIONAL SYSTEMS
ZERAOULIA ELHADJ
Department of Mathematics,
University of T´ebessa, 12002, Algeria
zeraoulia@mail.univ-tebessa.dz
zelhadj12@yahoo.fr
J. C. SPROTT
Department of Physics, University of Wisconsin,
Madison, WI 53706, USA
sprott@physics.wisc.edu
Received March 31, 2013; Revised July 10, 2013
ABSTRACT
In this letter, we will show the existence of invariant sets called
universal basins of attraction for typical nonlinear
high-dimensional dynamical systems such as randomly sampled
high-dimensional vector fields (ODEs) or maps. The method of
analysis is based on the definition of an equivalence class
between systems with the same number of neurons, the same number of
time lags, and the same upper bound for one family of bifurcation
parameters.
Ref: E. Zeraoulia and J. C. Sprott,
International Journal of Bifurcation and Chaos 23, 1350120 (2013)
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