Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications

Setti, Gianluca; Mazzini, G.; Rovatti, Riccardo; Callegari, Sergio

doi:10.1109/jproc.2002.1015001

Cited by 148 publications

(78 citation statements)

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“…In the companion paper [5], we have shown that coupling the properties of piecewise-affine Markov maps with the choice of observable functions that are constant in each of the intervals of the Markov partition leads to powerful results. In particular, we are able to fully characterize the joint probabilities needed to compute all kind of expectations of observables within the chosen family.…”

Section: Ideas For a More General Model Of Quantized Chaotic Evolmentioning

confidence: 99%

“…With this, finite as well as asymptotic properties of correlation functions depend on the spectral structure of , which is a finite matrix and can, therefore, be analyzed (and sometime designed) by elementary linear algebraic methods. When such correlation functions are the key factor in the performance of a system in which a chaotic component has been introduced (e.g., the DS-CDMA example in [5]), this gives us high chances of optimization by means of proper statistical chaos design.The success of such an approach now encourages us to consider more general piecewise-affine Markov maps in which the Markov partition is made of a nonnecessarily finite number of intervals. Despite their seeming a quite abstract exercise, these maps may be of nonnegligible interest even from the applicative point of view.…”

Section: Ideas For a More General Model Of Quantized Chaotic Evolmentioning

confidence: 99%

“…

I. SCENARIOS FOR ADVANCED APPLICATIONS

Modern information engineering deals with systems made of a population of active and often intelligent units deeply interconnected and interacting.

…”

mentioning

confidence: 99%

“…With the aim of explaining the formal development behind the chaos-based modeling of network traffic and other similar phenomena, here we generalize the tools presented in the companion paper (Setti et al, 2002) …”

mentioning

confidence: 99%

“…In fact, we will base our development on the concept of finite-dimensional projection of the operator supervising the statistical dynamics of chaotic systems [5].…”

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confidence: 99%

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Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications

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With the aim of explaining the formal development behind the chaos-based modeling of network traffic and other similar phenomena, here we generalize the tools presented in the companion paper (Setti et al., 2002) I. SCENARIOS FOR ADVANCED APPLICATIONSModern information engineering deals with systems made of a population of active and often intelligent units deeply interconnected and interacting. In fact, this paradigm applies to many of the most fundamental technologies supporting nowadays information society as well as many of the most advanced proposals for its evolution: from Ethernet-based local area networks (LANs) to frame-relay or asynchronous Manuscript received July 3, 2001; revised November 25, 2001. R. Rovatti is with CEG-ARCES, University of Bologna, 40136 Bologna, Italy (e-mail: r.rovatti@chaos.cc).G. Mazzini and G. Setti are with DEC-DI, University of Ferrara, 44100 Ferrara, Italy (e-mail: g.mazzini@ieee.org; gsetti@ing.unife.it) and also with CEG-ARCES, University of Bologna, 40136 Bologna, Italy.A. Giovanardi is with CED-DI, University of Ferrara, 44100 Ferrara, Italy (e-mail: agiovanardi@ing.unife.it).Publisher Item Identifier S 0018-9219(02)05243-X.transfer mode geographic links, from Internet and its protocols to wireless sensor networks, and from distributed memory or processing hierarchies to distributed cooperative computation.The complexity of the activities carried out in those systems and the number of independent and often unpredictable entities interacting with them forces the extensive use of statistical tools for their modeling and design. Hence, future successful development of related technologies will depend on our ability of characterizing stochastic processes of increased complexity.One of the most significant example comes from digital communication networks where the discovery of self-similar of fractal processes opened a definite chasm between classical traffic and queuing analysis and the most recent trends and methods.As discussed in [1], modeling techniques in this field were forced to evolve from classical Poisson processes, to renewal processes with finite variance of interarrival times, to Markov chain administrating the transition between some of those renewal processes.The present state of this evolution is the widely accepted second-order self-similar model [1], [2] from which most of the recent network traffic analysis originate.A key step in this analysis was the discovery that complex self-similar behaviors can be interpreted as the superimposition of elementary binary (ON-OFF) processes featuring heavy-tailed (i.e., very slowly decaying) distribution of ON or OFF times [3], [4].Researchers interested in an intuitive explanation of the nontrivial features of aggregated traffic identify each ON-OFF process with a different session-based network activity (e.g., session). Here, we are more interested in the mathematical structure that they provide to the overall process.In fact, we will describe how such an observation can be at least partially systematized in a gen...

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Section: Ideas For a More General Model Of Quantized Chaotic Evolmentioning

confidence: 99%

Section: Ideas For a More General Model Of Quantized Chaotic Evolmentioning

confidence: 99%

“…

I. SCENARIOS FOR ADVANCED APPLICATIONS

Modern information engineering deals with systems made of a population of active and often intelligent units deeply interconnected and interacting.

…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…In fact, we will base our development on the concept of finite-dimensional projection of the operator supervising the statistical dynamics of chaotic systems [5].…”

mentioning

confidence: 99%

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Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications

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Chaos in Communications

Yao

Chen

2003

Wiley Encyclopedia of Telecommunications

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This paper examines the roles in which chaos have been used in various approaches in communications. In the first approach, instead of modulating a periodic sinusoidal carrier as in conventional communications, various forms of modulation using an aperiodic chaotic waveform have been proposed. They include chaotic masking, dynamical feedback, chaotic switching, and different versions of chaos shift keying. Since these continuous‐time chaotic digital communication systems are modeled as stochastic nonlinear dynamical systems, the error probabilities of many of these systems do not have analytically tractable forms, but must be numerically evaluated using Ito/Stratonovich stochastic integrations. In the second approach, symbolic dynamics viewed as a “coarse‐grained” description of a chaotic dynamical system is exploited for modulating/coding of digital data. In the third approach, chaotic dynamics are viewed as analog channel encoders. In the fourth approach, communications using chaotic pulse‐position‐modulation are discussed. In the fifth approach, CDMA communication systems using spread sequences generated from chaotic dynamics are considered. Finally, in the sixth approach, the roles of chaos in laser communication and modeling of RF propagation effects for clutter and fading channel are discussed. Some comments are also provided on the practicality of various chaos‐based communication schemes.

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Application of Chaotic Modulation

Chau

Wang

2011

Chaos in Electric Drive Systems

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Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications

Cited by 148 publications

References 52 publications

Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications

Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications

Chaos in Communications

Application of Chaotic Modulation

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