Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.1, pp.71--80

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2000, Volume 3, Number 1, pp.71--80

The Use of Low Dimensional Models of Engineering Dynamical Systems.
Steven R. Bishop

The discovery of chaos in low dimensional dynamical systems has provided a renewed interest in dynamics. The advance in computer technology allows us to solve (numerically) nonlinear problems of ever-increasing complexity. In some instances the need to explain specific numerical evidence has, in turn, promoted a resurgence in theoretical issues which provide insight into dynamical and bifurcational complexity. This paper considers two case studies in which low dimensional models have proved useful in examining the dynamical response of engineering systems. In the first example a pendulum system is modelled which enables fine-scale quantitative details to be established, allowing the zones in parameter space to be identified in which various solutions occur. The second treatment is the `broad brush' modelling of fire growth in a room. Here fine-scale details are not available but a qualitative insight into the dynamics can be used to guide more complex investigations. This dual approach to modelling exemplifies the merits of low dimensional modelling.
Key words: the low dimensional dynamical systems, the parametrically excited pendulum, chaos.

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