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Localization of simple and complex dynamics in nonlinear systems

Localization of simple and complex dynamics in nonlinear systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Localization of simple and complex dynamics in nonlinear systems

Krishchenko, A.
Differential Equations , Volume 51 (11) – Dec 16, 2015
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References (29)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S001226611511004X
Publisher site
See Article on Publisher Site

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.

Journal

Differential Equations – Springer Journals

Published: Dec 16, 2015

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