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Localization Method of Compact Invariant Sets with Application to the Chua System

A. F. Gribov

Bauman Moscow State Technical University, 2-aya Baumanskaya ul., 5, 105005 Moscow, Russia

E-mail Address: alexandr-gribov@list.ru

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A. N. Kanatnikov

Bauman Moscow State Technical University, 2-aya Baumanskaya ul., 5, 105005 Moscow, Russia

E-mail Address: skipper@bmstu.ru

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A. P. Krishchenko

Bauman Moscow State Technical University, 2-aya Baumanskaya ul., 5, 105005 Moscow, Russia

E-mail Address: apkri@bmstu.ru

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https://doi.org/10.1142/S0218127416500735Cited by:4 (Source: Crossref)

Abstract

In this paper, we consider the problem of compact invariant sets localization for the Chua system. To obtain our results we develop and apply a localization method. This method allows us to find two types of subsets in the phase space of a nonlinear system. The first type consists of Poincaré sections having a nonempty intersection with any compact invariant set of the system. The second type consists of localizing sets containing all compact invariant sets of the system. The considered localization method produces systems of inequalities describing the localizing sets and specifies the equations of the appropriate global sections. These inequalities and equations depend on parameters of the system and, therefore, the obtained localization results can be used in the bifurcation analysis. We find one-parametric families of both compact global sections and nontrivial localizing sets for the Chua system. These localizing sets are compact or unbounded. The intersection of unbounded localizing sets in some cases is a compact localizing set. We indicate the domains where trajectories of the Chua system go to infinity.

Keywords:

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