Hidden attractor in smooth Chua systems

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.

► There are hidden oscillations: basin does not contain neighborhoods of equilibria.
► Firstly hidden oscillations were found in systems with piecewise-linear nonlinearity.
► We show that hidden attractors can exist in systems with smooth nonlinearity.
► We suggest localization methods and find hidden attractors in a smooth Chua’s system.