3,370 research outputs found
Public channel cryptography by synchronization of neural networks and chaotic maps
Two different kinds of synchronization have been applied to cryptography:
Synchronization of chaotic maps by one common external signal and
synchronization of neural networks by mutual learning. By combining these two
mechanisms, where the external signal to the chaotic maps is synchronized by
the nets, we construct a hybrid network which allows a secure generation of
secret encryption keys over a public channel. The security with respect to
attacks, recently proposed by Shamir et al, is increased by chaotic
synchronization.Comment: 4 page
Higher order Dependency of Chaotic Maps
Some higher-order statistical dependency aspects
of chaotic maps are presented. The autocorrelation
function (ACF) of the mean-adjusted squares, termed the
quadratic autocorrelation function, is used to access nonlinear
dependence of the maps under consideration. A simple
analytical expression for the quadratic ACF has been
found in the case of fully stretching piece-wise linear maps.
A minimum bit energy criterion from chaos communications
is used to motivate choosing maps with strong negative
quadratic autocorrelation. A particular map in this
class, a so-called deformed circular map, is derived which
performs better than other well-known chaotic maps when
used for spreading sequences in chaotic shift-key communication
systems
Bifurcations in Globally Coupled Chaotic Maps
We propose a new method to investigate collective behavior in a network of
globally coupled chaotic elements generated by a tent map. In the limit of
large system size, the dynamics is described with the nonlinear
Frobenius-Perron equation. This equation can be transformed into a simple form
by making use of the piecewise linear nature of the individual map. Our method
is applied successfully to the analyses of stability of collective stationary
states and their bifurcations.Comment: 12 pages, revtex, 10 figure
Anticipating the dynamics of chaotic maps
We study the regime of anticipated synchronization in unidirectionally
coupled chaotic maps such that the slave map has its own output reinjected
after a certain delay. For a class of simple maps, we give analytic conditions
for the stability of the synchronized solution, and present results of
numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that
agree well with the analytic predictions.Comment: Uses the elsart.cls (v2000) style (included). 9 pages, including 4
figures. New version contains minor modifications to text and figure
Synchronization learning of coupled chaotic maps
We study the dynamics of an ensemble of globally coupled chaotic logistic
maps under the action of a learning algorithm aimed at driving the system from
incoherent collective evolution to a state of spontaneous full synchronization.
Numerical calculations reveal a sharp transition between regimes of
unsuccessful and successful learning as the algorithm stiffness grows. In the
regime of successful learning, an optimal value of the stiffness is found for
which the learning time is minimal
Fractal Weyl Law for Open Chaotic Maps
This contribution summarizes our work with M.Zworski on open quantum open
chaoticmaps (math-ph/0505034). For a simple chaotic scattering system (the open
quantum baker's map), we compute the "long-living resonances" in the
semiclassical r\'{e}gime, and show that they satisfy a fractal Weyl law. We can
prove this fractal law in the case of a modified model.Comment: Contribution to the Proceedings of the conference QMath9,
Mathematical Physics of Quantum Mechanics, September 12th-16th 2004, Giens,
Franc
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