Non-invertible transformations and spatiotemporal randomness

Details Non-invertible transformations and spatiotemporal randomness Non-invertible transformations and spatiotemporal randomness

2006-02-12

arxiv.org/abs/nlin/0602026v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

Accepted in International Journal of Bifurcation and Chaos

Scientific paper

We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems can generate random dynamics. For instance, the chaotic Chua's circuit coupled to a circuit with a non-invertible I-V characteristic can generate unpredictable dynamics. In general, a nonperiodic time-series with truncated exponential behavior can be converted into unpredictable dynamics using non-invertible transformations. Using a new theoretical framework for chaos and randomness, we investigate some classes of coupled map lattices. We show that, in some cases, these systems can produce completely unpredictable dynamics. In a similar fashion, we explain why some wellknown spatiotemporal systems have been found to produce very complex dynamics in numerical simulations. We discuss real physical systems that can generate random dynamics.

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