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Erschienen in:
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2015 | OriginalPaper | Buchkapitel

2. Dynamical Systems

verfasst von : Anthony N. Michel, Ling Hou, Derong Liu

Erschienen in: Stability of Dynamical Systems

Verlag: Springer International Publishing

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Abstract

We give the definition of dynamical system and a classification of such systems: finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous and discontinuous systems; autonomous and non-autonomous systems; and composite systems. Classes of finite-dimensional dynamical systems that we address include systems determined by ordinary differential equations, ordinary differential inequalities, ordinary difference equations, and ordinary difference inequalities. General classes of infinite-dimensional dynamical systems that we address include systems determined by differential equations and inclusions defined on Banach spaces and systems determined by linear and nonlinear semigroups. Specific classes of infinite-dimensional dynamical systems that we address include systems determined by functional differential equations, Volterra integrodifferential equations, and certain classes of partial differential equations. For all cases, we present specific examples.

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Vorheriges Kapitel Introduction
Nächstes Kapitel Fundamental Theory: The Principal Stability and Boundedness Results on Metric Spaces
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Metadaten
Titel
Dynamical Systems
verfasst von
Anthony N. Michel
Ling Hou
Derong Liu
Copyright-Jahr
2015
Buch
Stability of Dynamical Systems

Print ISBN: 978-3-319-15274-5

Electronic ISBN: 978-3-319-15275-2

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-15275-2_2

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