RESUMO
It has recently been emphasized again that the very existence of stationary stable localized structures with short-range interactions might allow one to store information in nonequilibrium media, opening new perspectives on information storage. We show how to use generalized topological entropies to measure aspects of the quantities of storable and nonstorable information. This leads us to introduce a measure of the long-term stably storable information. As a first example to illustrate these concepts, we revisit a mechanism for the appearance of stationary stable localized structures that is related to the stabilization of fronts between structured and unstructured states (or between differently structured states).
Assuntos
Computadores Moleculares , Metodologias Computacionais , Armazenamento e Recuperação da Informação/métodos , Entropia , Computação Matemática , Dinâmica não Linear , SoftwareRESUMO
In this paper we describe how to use the bifurcation structure of static localized solutions in one dimension to store information on a medium in such a way that no extrinsic grid is needed to locate the information. We demonstrate that these principles, deduced from the mathematics adapted to describe one-dimensional media, also allow one to store information on two-dimensional media.
Assuntos
Computadores Moleculares , Metodologias Computacionais , Armazenamento e Recuperação da Informação/métodos , Processamento de Sinais Assistido por Computador , Dinâmica não LinearRESUMO
We study the existence, the stability properties, and the bifurcation structure of static localized solutions in one dimension, near the robust existence of stable fronts between homogeneous solutions and periodic patterns.
RESUMO
When a map has one positive Lyapunov exponent, its attractors often look like multidimensional, Cantorial plates of spaghetti. What saves the situation is that there is a deterministic jumping from strand to strand. We propose to approximate such attractors as finite sets of K suitably prescribed curves, each parametrized by an interval. The action of the map on each attractor is then approximated by a map that takes a set of curves into itself, and we graph it on a KxK checkerboard as a discontinuous one-dimensional map that captures the quantitative dynamics of the original system when K is sufficiently large. (c) 1995 American Institute of Physics.
