### Hans H. Diebner's Research

## Rössler Attractor: Mixing

10000 initial states are set within a narrow environment, which reflects an uncertainty in measurement. When following-up these points under the impact of the Rössler dynamics, the cloud of points expands more and more until it is distributed over the whole attractor. This representation shows the divergence of neighbored states within the attractor, i.e., the mixing feature typical for chaos can be observed. Thereby, also the ergodic characteristic of a chaotic system is visualised. The distribution of state points (which is a densitiy in the limit case) corresponds to the ensemble average which in turn is equal to the temporal average resulting from the density of a single trajectory. Confer the trajectory of the Rössler system.Bifurcation parameter b = 5.6 (use slider to control)

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*Menu for pre-set values of the bifurcation parameters b:*

Period-1-Orbit

Period-2-Orbit

Period-4-Orbit

Period-8-Orbit

Chaos (Period-infinity, i.e. a-periodic)

marginally stable Period-3-Orbit (periodic window within chaos) with chaotic intermittency.

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