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On Existence of Simple Invariant Contours in Invariant Sets of Nonlinear Dynamic Systems of the Second Order

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Abstract

Consideration was given to existence of simple invariant closed curves (simple contours) in the invariant m-connected compact sets with the interior of the phase plane for an arbitrary number m. The lower bound of the number of contours in these sets was established. Invariance and m-connectivity of the compact set with the interior was shown to be the sufficient condition for existence of at least m simple invariant contours in it.

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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. On Existence of Simple Invariant Contours in Invariant Sets of Nonlinear Dynamic Systems of the Second Order. Automation and Remote Control 63, 375–387 (2002). https://doi.org/10.1023/A:1014742131616

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  • DOI: https://doi.org/10.1023/A:1014742131616

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