Abstract
A principal new direction in the study of complex systems is through qualitative descriptions of the behaviour. Typically a system is modelled by a state space and a flow. The flow tells us how the state of the system changes with time. A lot can be said about the qualitative behaviour of the system by the geometry of the flow, in particular the geometry of the attractors in the flow. There are just a few elementary attractors: equilibria, periodic and quasi-periodic, which have the simple geometry of points, lines and surfaces. However there are also chaotic behaviours arising from strange attractors which have a fractal geometry. The behaviour of a system of interconnected elementary and chaotic subsystems will be described, in particular the change of the fractal dimension, a measure of how chaotic the system is.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Guckenheimer J. and Holmes P., 1986, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York.
Hirsch M. and Smale P., 1974, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York.
Judd K., 1989, The Structure and Dimension of Strange Attractors, Ph.D. Thesis, The University of Western Australia.
Mees A.I., 1981, Dynamics of Nonlinear Feedback Systems Wiley, Cambridge.
Salam F et al, 1983, Chaos and Arnold Diffusion in Dynamical Systems, IEEE Transactions on Circuits and Systems, CAS-30, No 9.
Sparrow C.,1982, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Apppl. Math. Sci. 41. Springer-Verlag, New York.
Takens F., 1980, Detecting Strange Attractor in Turbulence., Dynamical Systems and Turbulence. Lecture Notes in Mathematics. Vol. 898, Rand D.A. and Young L.S., eds, pp. 365–381. Springer-Verlag, New York.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
Judd, K. (1990). Chaos in Complex Systems. In: Vincent, T.L., Mees, A.I., Jennings, L.S. (eds) Dynamics of Complex Interconnected Biological Systems. Mathematical Modelling, vol 6. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6784-0_8
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6784-0_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-6786-4
Online ISBN: 978-1-4684-6784-0
eBook Packages: Springer Book Archive