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1.
Chaos ; 14(3): 839-44, 2004 Sep.
Article in English | MEDLINE | ID: mdl-15446994

ABSTRACT

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).


Subject(s)
Computers, Molecular , Computing Methodologies , Information Storage and Retrieval/methods , Entropy , Mathematical Computing , Nonlinear Dynamics , Software
2.
Chaos ; 14(1): 193-8, 2004 Mar.
Article in English | MEDLINE | ID: mdl-15003061

ABSTRACT

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.


Subject(s)
Computers, Molecular , Computing Methodologies , Information Storage and Retrieval/methods , Signal Processing, Computer-Assisted , Nonlinear Dynamics
3.
Phys Rev Lett ; 84(14): 3069-72, 2000 Apr 03.
Article in English | MEDLINE | ID: mdl-11019014

ABSTRACT

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.

4.
Chaos ; 5(1): 216-226, 1995 Mar.
Article in English | MEDLINE | ID: mdl-12780176

ABSTRACT

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.

5.
Phys Rev Lett ; 72(1): 80-83, 1994 Jan 03.
Article in English | MEDLINE | ID: mdl-10055571
6.
Phys Rev Lett ; 70(3): 279-282, 1993 Jan 18.
Article in English | MEDLINE | ID: mdl-10054072
7.
Phys Rev A Gen Phys ; 35(4): 1884-1900, 1987 Feb 15.
Article in English | MEDLINE | ID: mdl-9898355
8.
Phys Rev Lett ; 57(8): 925-928, 1986 Aug 25.
Article in English | MEDLINE | ID: mdl-10034201
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