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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Dynamical Systems with Dissipation
verfasst von : John Argyris (Deceased), Gunter Faust, Maria Haase, Rudolf Friedrich (Deceased)
Erschienen in: An Exploration of Dynamical Systems and Chaos
Verlag: Springer Berlin Heidelberg
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In the preceding chapter, we discussed conservative, i.e. dissipation-free, dynamical systems. This category of physical or mechanical systems is characterised by the fact that a volume of an element in the phase space remains invariant, (see eq. (4.1.30), Liouville theorem). In this chapter, we expand our theoretical considerations and deal with non-linear dissipative systems, i.e. dynamical systems experiencing a loss of energy. If we again observe a volume element in the phase space, then, for t
t
→ ∞, it will contract to a subset of an attractor, the dimensionality of which is lower than that of the phase space.