Chaos in Complex Systems
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.
KeywordsChaotic System Bifurcation Diagram Chaotic Behaviour Unstable Manifold Strange Attractor
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