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Localization of simple and complex dynamics in nonlinear systems

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Abstract

We consider problems of finding subsets (localizing sets) that contain all compact invariant sets in the state spaces of time-invariant and time-varying systems of differential equations. We describe the behavior of trajectories outside localizing sets corresponding to localizing functions. We obtain conditions under which the phase portrait of the system has a simple structure outside localizing sets and all singularities are concentrated in localizing sets. As an example, we consider the Duffing equation with an uncertain bounded external input, for which we find compact localizing sets, present an example of their computation, and describe the behavior of trajectories outside localizing sets.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, Russia

    A. P. Krishchenko

  2. Institute for Systems Analysis of Russian Academy of Sciences, Moscow, Russia

    A. P. Krishchenko

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  1. A. P. Krishchenko
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Correspondence to A. P. Krishchenko.

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Original Russian Text © A.P. Krishchenko, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 11, pp. 1440–1447.

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Krishchenko, A.P. Localization of simple and complex dynamics in nonlinear systems. Diff Equat 51, 1432–1439 (2015). https://doi.org/10.1134/S001226611511004X

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  • DOI: https://doi.org/10.1134/S001226611511004X

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