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Hidden attractor in smooth Chua systems. (English) Zbl 1277.34052
Summary: 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.

MSC:
34C28 Complex behavior and chaotic systems of ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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