L P Kadanoff | PubMed Health

PubMed1999

Noise stabilization of self-organized memories.

We investigate a nonlinear dynamical system which "remembers" preselected values of a system parameter. The deterministic version of the system can encode many parameter values during a transient period, but in the limit of long times, almost all of them are forgotten. Here we show that a certain type of stochastic noise can stabilize multiple memories, enabling many parameter values to be encoded permanently. We present analytic results that provide insight both into the memory formation and into the noise-induced memory stabilization. The relevance of our results to experiments on the charge-density wave material NbSe3 is discussed.

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PubMed1984

Escape from strange repellers.

In a dynamical system described by a map, it may be that a "strange" sets of points is left invariant under the mapping. The set is a repeller if points placed in its neighborhood move away. An escape rate is defined to describe this motion. An alternative method of evaluating the escape rate, based on the consideration of repulsive cycles, is proposed. In the several cases examined numerically and analytically, the escape rate is shown to agree with the proposed formula.

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