Preservation of stability of dynamical systems under homomorphisms

For abstract dynamical systems in the form of systems of motions, we obtain criteria for the preservation of stability properties via an extended notion of a homomorphism of dynamical systems. We obtain corollaries for ordinary differential equations including those with switchings of vector fields....

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Bibliographic Details
Published in:	Differential equations Vol. 45; no. 12; pp. 1709 - 1720
Main Authors:	Vassilyev, S. N., Ul’yanov, S. A.
Format:	Journal Article
Language:	English
Published:	Dordrecht SP MAIK Nauka/Interperiodica 01-12-2009 Springer Nature B.V
Subjects:	Coordinate transformations Difference and Functional Equations Differential equations Dynamical systems Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Studies Vector space Lyapunov Function Model Transformation Hybrid System Vector Lyapunov Function Initial Time Instant
Online Access:	Get full text
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Summary:	For abstract dynamical systems in the form of systems of motions, we obtain criteria for the preservation of stability properties via an extended notion of a homomorphism of dynamical systems. We obtain corollaries for ordinary differential equations including those with switchings of vector fields. We present examples illustrating the use of these criteria.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266109120015