1,155 research outputs found
Noise robustness condition for chaotic maps with piecewise constant invariant density
3noChaotic maps represent an effective method for generating random-like sequences, that combines the benefits of relying on simple, causal models with good unpredictability. Regrettably such positive features are counterbalanced by the fact that statistics of true-implemented chaotic maps are generally strongly dependent on implementation errors and external perturbations. Here we study the effect of an external, additive, map-independent noise perturbation in the map model, and present a technique to guarantee, for a quite large class of maps, independence of the first-order statistics of the noise features.partially_openopenPareschi F.; Setti G.; Rovatti R.Pareschi, F.; Setti, G.; Rovatti, R
Quantifiers for randomness of chaotic pseudo random number generators
We deal with randomness quantifiers and concentrate on their ability to discern the hallmark of chaos in time series used in connection with pseudo-random number generators (PRNGs). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely (i) its invariant measure and (ii) the mixing constant. This is of help in answering two questions that arise in applications: (i) which is the best PRNG among the available ones? and (ii) if a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure? Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.Instituto de Física La Plat
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Chaotic and fractal properties of deterministic diffusion-reaction processes
We study the consequences of deterministic chaos for diffusion-controlled
reaction. As an example, we analyze a diffusive-reactive deterministic
multibaker and a parameter-dependent variation of it. We construct the
diffusive and the reactive modes of the models as eigenstates of the
Frobenius-Perron operator. The associated eigenvalues provide the dispersion
relations of diffusion and reaction and, hence, they determine the reaction
rate. For the simplest model we show explicitly that the reaction rate behaves
as phenomenologically expected for one-dimensional diffusion-controlled
reaction. Under parametric variation, we find that both the diffusion
coefficient and the reaction rate have fractal-like dependences on the system
parameter.Comment: 14 pages (revtex), 12 figures (postscript), to appear in CHAO
Chaotic macroscopic phases in one-dimensional oscillators
APo and EU wish to acknowledge the Advanced Study Group activity at the Max Planck Institute for the Physics of Complex Systems in Dresden “From Microscopic to Collective Dynamics in Neural Circuits” for the opportunity to develop part of the project.Peer reviewedPublisher PD
Integrated chaos generators
This paper surveys the different design issues, from mathematical model to silicon, involved on the design of integrated circuits for the generation of chaotic behavior.Comisión Interministerial de Ciencia y Tecnología 1FD97-1611(TIC)European Commission ESPRIT 3110
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