Chaos

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Summary

In this lecture we made the acquaintance of deterministic chaos as a property of nonlinear systems. It is characterised by a strong dependence on the initial parameters such that small deviations lead to huge effects. We quantified these effects through Lyapunov exponents, and we analysed the chaotic behaviour through phase space maps, also. Ultimately, we analysed in somewhat more detail one way that the pendulum turns chaotic, namely period doubling. This road is one typical way of how chaotic systems make the transition from a non-chaotic to a chaotic regime. We briefly discussed a graphical representation, the bifurcation diagram, and we learned that this road to chaos is truly universal, when realised, characterised by a universal constant.

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Frank Krauss and Daniel Maitre
Last modified: Tue Oct 3 14:43:58 BST 2017