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Method of Radial Drift for Qualitative Study of the Properties of the Nonlinear Dynamic Systems. III. On Existence of Invariant Closed Contours

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Abstract

Consideration was given to existence of the invariant closed contours of the nonlinear autonomous dynamic systems, that is, the closed contours consisting wholly of the trajectories of dynamic systems obeying the ordinary nonlinear vector differential equations of an arbitrary order. The structure of these contours was studied, and their classification was elaborated. Efficient conditions for nonexistence and existence of the invariant contours were obtained. Studies were carried out using the method of radial drift.

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  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    V. P. Zhukov

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  1. V. P. Zhukov
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Zhukov, V.P. Method of Radial Drift for Qualitative Study of the Properties of the Nonlinear Dynamic Systems. III. On Existence of Invariant Closed Contours. Automation and Remote Control 62, 1240–1258 (2001). https://doi.org/10.1023/A:1010245310060

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  • DOI: https://doi.org/10.1023/A:1010245310060

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