Deterministic chaos

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Deterministic chaos is a random behavior of a dynamic system , which however follows deterministic rules. Dynamic systems with deterministic chaotic behavior are only apparently stochastic systems . The behavior is not caused by random external circumstances such as noise . It follows from the properties of the system itself.

The behavior of physical systems that show deterministic chaos cannot be predicted in the long term. Their behavior is not reproducible . This non-reproducibility despite deterministic dynamics is a consequence of the fact that the starting conditions of a real physical system cannot be exactly repeated. That is, for chaotic dynamic systems , similar causes do not lead to similar effects in the long term. This fact is known as the butterfly effect.

In the analysis of non-periodic processes, both statistical methods and methods from chaos research are used. In order to detect deterministic chaos in a randomly appearing time series, methods such as spectral analysis using Fourier transformation , delay diagrams ( Hénon mapping ; close pairs), iterated function systems (IFS) and neural networks are used.

The non-linear , discrete-time logistic equation is a particularly simple system that can show deterministic chaos.

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