Exploiting Nonlinear Dynamics to Store and Process Information

@article{Miliotis2008ExploitingND,
  title={Exploiting Nonlinear Dynamics to Store and Process Information},
  author={Abraham Miliotis and Sudeshna Sinha and William L. Ditto},
  journal={Int. J. Bifurc. Chaos},
  year={2008},
  volume={18},
  pages={1551-1559}
}
By applying nonlinear dynamics to the dense storage of information, we demonstrate how a single nonlinear dynamical element can store M items, where M is variable and can be large. This provides the capability for naturally storing data in different bases or in different alphabets and can be used to implement multilevel logic. Further we show how this method of storing information can serve as a preprocessing tool for (exact or inexact) pattern matching searches. Since our scheme involves just… Expand
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References

SHOWING 1-10 OF 26 REFERENCES
DYNAMICS BASED COMPUTATION
We demonstrate the ability of lattices of coupled chaotic maps to perform simple computations. This dynamical system is shown to emulate logic gates, encode numbers, and perform specific arithmeticExpand
Using thresholding at varying intervals to obtain different temporal patterns.
  • S. Sinha
  • Medicine, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
It is evident that thresholding is capable of yielding exact limit cycles of varying periods and geometries when implemented at different intervals (even when very infrequent), which suggests a simple and potent mechanism for selecting different regular temporal patterns from chaotic dynamics. Expand
Flexible parallel implementation of logic gates using chaotic elements.
TLDR
The proposed parallel computing architecture is implemented to obtain parallelized bit-by-bit addition with a two-dimensional chaotic neuronal and a three- dimensional chaotic laser model to demonstrate the parallelism inherent in such systems. Expand
Chaos computing: implementation of fundamental logical gates by chaotic elements
Basic principles of implementing the most fundamental computing functions by chaotic elements are described. They provide a theoretical foundation of computer architecture based on a totally newExpand
Computing with distributed chaos.
  • S. Sinha, W. Ditto
  • Medicine, Mathematics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
TLDR
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. Expand
Nonlinearity and computation: implementing logic as a nonlinear dynamical system
Abstract Recently, Sinha and Ditto [Phys. Rev. Lett. 81 (1998) 2156] demonstrated the computational possibilities of an array of coupled maps. We generalize this nonlinear dynamical system to improveExpand
Associative processing and processors
TLDR
Associative memory provides a naturally parallel and scalable form of data retrieval for both structured data and unstructured data, and can be easily extended to process the retrieved data in place, thus becoming an associative processor. Expand
Experimental realization of chaos control by thresholding.
  • K. Murali, S. Sinha
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
The experimental verification of thresholding as a versatile tool for efficient and flexible chaos control is reported, and the ease and rapidity of switching between different targets it offers, suggests a potent tool for chaos based applications. Expand
Parallel computing with extended dynamical systems.
TLDR
The scope of parallelism based on extended dynamical systems, in particular, arrays of chaotic elements, is discussed, and the rapid solution of the Deutsch-Jozsa problem is demonstrated utilizing the collective properties of such systems. Expand
New Method for the Control of Fast Chaotic Oscillations
We introduce a new method of controlling chaos that retains the essential features of occasional proportional feedback, but is much simpler to implement. We demonstrate control on a simpleExpand
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