Two qualitatively different types of dynamical behaviour can be so tightly interwoven that it becomes impossible to predict when a small change in parameters will cause a change in qualitative properties. For Quadratic mappings of the interval, for example, the chaotic parameter vales form a Cantor set of positive measure, broken up by periodic intervals. This set can be described by a global scaling law, which makes it possible to form a good estimate of the fraction of chaotic parameter values. Sensitive dependence on parameters occurs when the scaling exponent is conjectures to display universal behaviour.


Farmer, J.D. (1985). 'Sensitive Dependence on Parameters in Nonlinear Dynamics'. Physical Review Letters, 55(4), pp.351-355.
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