Journal ArticleDOI
Coupled map lattices as computational systems
TLDR
It is shown that the CML is a valid new model for a parallel deterministic analog machine, but that, in principle, such a CML computer does not generate computations that cannot be reproduced by the standard mathematical models for computing on real numbers.Abstract:
The coupled map lattice (CML) as a mathematical model for a computer is considered. Using the theory of synchronous concurrent algorithms, it is shown that the CML is a valid new model for a parallel deterministic analog machine, but that, in principle, such a CML computer does not generate computations that cannot be reproduced by the standard mathematical models for computing on real numbers. The analysis is based on new general mathematical definitions of CMLs, and an axiomatic approach to determining which models of computation can be used to simulate CMLs.read more
Citations
More filters
Journal ArticleDOI
A survey of stream processing
TL;DR: An analysis of the development of each of these specialized topics to determine if a general theory of stream processing has emerged is presented, including a comparison of the semantic models that are used to formalize stream based computation.
Journal ArticleDOI
An introduction to chaotic dynamical systems (2nd edition), by Robert L. Devaney. Pp 336. £34·95. 1989. ISBN 0-201-13046-7 (Addison-Wesley)
TL;DR: In this paper, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Journal ArticleDOI
Computing with distributed chaos.
Sudeshna Sinha,William L. Ditto +1 more
TL;DR: The capacity of a lattice of threshold coupled chaotic maps to perform computations is demonstrated, and the scheme is extended to multidimensional continuous time dynamics, in particular to a system relevant to chaotic lasers.
Journal ArticleDOI
The bifurcating neuron network 1
Geehyuk Lee,Nabil H. Farhat +1 more
TL;DR: A preliminary study on the tri-stability of the BN, the behaviors of interacting such BNs, and a design of a network of BNs that interact via "mutually-exclusive" coupling, thereby solving a 3-coloring problem are reported.
Journal ArticleDOI
Coupled map lattices: one step forward and two steps back
TL;DR: In this article, the general notion of lattice dynamical systems is discussed and some recent progress in their studies are discussed, as well as the approach that allows to extract some information on the dynamics of finitely extended (real) systems from the results obtained on the infinitely extended (artificial) ones.
References
More filters
Journal ArticleDOI
Theory of Recursive Functions and Effective Computability.
Solomon Feferman,Hartley Rogers +1 more
TL;DR: Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.
Book
An introduction to chaotic dynamical systems
TL;DR: In this article, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Book
Iterated maps on the interval as dynamical systems
TL;DR: In this article, the Calculus of itineraries is used to describe the properties of one-parameter families of maps and the relative frequency of periodic and aperiodic behavior.