Dynamical Systems with Dissipation

Abstract

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.