2,830 research outputs found
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
In this set of lectures, we review briefly some of the recent developments in
the study of the chaotic dynamics of nonlinear oscillators, particularly of
damped and driven type. By taking a representative set of examples such as the
Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain
the various bifurcations and chaos phenomena associated with these systems. We
use numerical and analytical as well as analogue simulation methods to study
these systems. Then we point out how controlling of chaotic motions can be
effected by algorithmic procedures requiring minimal perturbations. Finally we
briefly discuss how synchronization of identically evolving chaotic systems can
be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in
Physics Please Lakshmanan for figures (e-mail: [email protected]
Karhunen-Lo`eve Decomposition of Extensive Chaos
We show that the number of KLD (Karhunen-Lo`eve decomposition) modes D_KLD(f)
needed to capture a fraction f of the total variance of an extensively chaotic
state scales extensively with subsystem volume V. This allows a correlation
length xi_KLD(f) to be defined that is easily calculated from spatially
localized data. We show that xi_KLD(f) has a parametric dependence similar to
that of the dimension correlation length and demonstrate that this length can
be used to characterize high-dimensional inhomogeneous spatiotemporal chaos.Comment: 12 pages including 4 figures, uses REVTeX macros. To appear in Phys.
Rev. Let
Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations
We present results from an experiment similar to one performed by Packard
(1988), in which a genetic algorithm is used to evolve cellular automata (CA)
to perform a particular computational task. Packard examined the frequency of
evolved CA rules as a function of Langton's lambda parameter (Langton, 1990),
and interpreted the results of his experiment as giving evidence for the
following two hypotheses: (1) CA rules able to perform complex computations are
most likely to be found near ``critical'' lambda values, which have been
claimed to correlate with a phase transition between ordered and chaotic
behavioral regimes for CA; (2) When CA rules are evolved to perform a complex
computation, evolution will tend to select rules with lambda values close to
the critical values. Our experiment produced very different results, and we
suggest that the interpretation of the original results is not correct. We also
review and discuss issues related to lambda, dynamical-behavior classes, and
computation in CA. The main constructive results of our study are identifying
the emergence and competition of computational strategies and analyzing the
central role of symmetries in an evolutionary system. In particular, we
demonstrate how symmetry breaking can impede the evolution toward higher
computational capability.Comment: 38 pages, compressed .ps files (780Kb) available ONLY thru anonymous
ftp. (Instructions available via `get 9303003' .
Photonic reservoir computing: a new approach to optical information processing
Despite ever increasing computational power, recognition and classification problems remain challenging to solve. Recently advances have been made by the introduction of the new concept of reservoir computing. This is a methodology coming from the field of machine learning and neural networks and has been successfully used in several pattern classification problems, like speech and image recognition. The implementations have so far been in software, limiting their speed and power efficiency. Photonics could be an excellent platform for a hardware implementation of this concept because of its inherent parallelism and unique nonlinear behaviour. We propose using a network of coupled Semiconductor Optical Amplifiers (SOA) and show in simulation that it could be used as a reservoir by comparing it on a benchmark speech recognition task to conventional software implementations. In spite of several differences, they perform as good as or better than conventional implementations. Moreover, a photonic implementation offers the promise of massively parallel information processing with low power and high speed. We will also address the role phase plays on the reservoir performance
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