Hidden attractor in smooth Chua systems

作者:Leonov, G. A.; Kuznetsov, N. V.*; Vagaitsev, V. I.
来源:Physica D: Nonlinear Phenomena , 2012, 241(18): 1482-1486.
DOI:10.1016/j.physd.2012.05.016

摘要

The hidden oscillations (a basin of attraction of which does not contain neighborhoods of equilibria) have been obtained first in the 50-60s of the 20th century in automatic control systems with scalar piecewise-linear nonlinearity. This brings up the question about the excitation nature of hidden oscillations. @@@ In the present paper it is shown that hidden oscillations can exist not only in systems with piecewise-linear nonlinearity but also in smooth systems. Here the possibility of the existence of a hidden chaotic attractor in a modified Chua's system with a smooth characteristic of nonlinear element is demonstrated.