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Localization of hidden attractors of the generalized Chua system based on the method of harmonic balance. (English. Russian original) Zbl 1251.37081
Vestn. St. Petersbg. Univ., Math. 43, No. 4, 242-255 (2010); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 2010, No. 4, 62-76 (2010).
Summary: Chua’s circuits, which were introduced by Leon Ong Chua in 1983, are simplest electric circuits operating in the mode of chaotic oscillations. Systems of differential equations describing the behavior of Chua’s circuits are three-dimensional autonomous dynamical systems with scalar nonlinearity. In the standard Chua system, chaotic oscillations are excited in the classical manner, namely, starting from the neighborhood of the unstable zero equilibrium, after the transient process, the system trajectory tends to a Chua attractor.
In this work, generalized Chua systems (i.e., Chua systems with a locally stable equilibrium) are considered. In such systems, the above mentioned method for detection of attractors fails to work. In 2008 G.A. Leonov suggested an analytical-numerical approach to searching for periodic solutions in autonomous dynamical systems with scalar nonlinearity. This method combines the standard method of harmonic balance, the classical method of small parameter, bifurcation theory, and numerical methods. In this work, the method suggested is used for numerical localization of hidden attractors of a generalized Chua system.

MSC:
37N35 Dynamical systems in control
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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