1,721,126 research outputs found
Statistical features and robustness of chaotic fuzzy maps
No full textThe properties of the discrete-time nonlinear dynamics induced by a fuzzy system are investigated. Nonlinear dynamical system theory tools are applied to give conditions for fuzzy maps to produce sufficiently complex but asymptotically definite behavior and an approximation scheme allowing its statistical characterization is discussed. Then, to allow the application of synthesis and implementation methodologies for fuzzy systems to the realization of nontrivial or even chaotic dynamics we also give a novel and effective result on the robustness of that statistical characterization with respect to small perturbations or to certain implementation non-idealities
Topological conjugacy propagates stochastic robustness of chaotic maps
No full textWe here consider an extension of the validity of classical criteria ensuring the robustness of the statistical features of discrete time dynamical systems with respect to implementation inaccuracies and noise. The result is achieved by proving that, whenever a discrete time dynamical system is robust, all the discrete time dynamical systems topologically conjugate with it are also robust. In particular, this result offer an explanation for the stochastic robustness of the logistic map, which is confirmed by the reported experimental measurements. key words: Chaotich maps implementation, robustness, statistical dynamical system theory
On the distribution of synchronization delays in coupled fully-stretching markov maps
No full textSynchronization between two fully stretching piecewise affine Markov maps in the usual master-slave configuration has been proven to be possible in some interesting 2-dimensional and 3-dimensional cases [1], [2]. Aim of this contribution is to make a further step in the study of this phenomenon by showing that, if the two systems synchronize, the probability of having a certain synchronization time is bounded from above by an exponentially vanishing distribution. This result gives some formal ground to the numerical evidence shown in [2]
A tensor approach to higher order expectations of quantized chaotic trajectories - part I: general theory and specialization to piecewise affine markov systems
No full textThe problem of computing any-order expectations of trajectories generated by discrete-time one-dimensional chaotic systems is addressed by means of a suitable generalization of the Perron–Frobenius operator and its quantization. Tools from tensor algebra are introduced and analytical expressions for the special case of piecewise-affine Markov maps are obtained. Results are further specialized for a family of maps with quite general features.
As an example application, some cross- and self-interference terms are computed, which are involved in the evaluation of the performance of chaos-based DS-CDMA systems in an asynchronous multipath environment
Multimode time-Markov systems: Recursive tensor-based analysis, chaotic generation, locally looping processes
No full textThe paper proposes a systematic solution to the problem of mixing different stochastic processes, each implied by a certain mode of operation of the system at hand and with a random duration whose distribution depends on the previous and present modes. We do so by widening the scope of an existing framework for the statistical characterization of finite valued processes with memory-one properties. The point of view is that of stochastic dynamics and the state space of the process is partitioned into regions (that we identify with modes) such that, if sojourn in a mode can be assumed, the statistical characterization is fully understood. The process is also allowed to stochastically move from one mode to another and the number of time steps for which it remains in each mode is a random variable whose distribution is a function only of the mode visited before. A general theoretical framework is developed here for the computation of any-order joint probabilities. The framework is then exemplified for the case of locally looping systems that are random sequences of modes comprising the cyclical execution of given atomic actions. They are the model of choice for complex appliances that operate following the steps of a communication protocol, and/or the various phases of a bus cycle, and/or the load-computestore mechanism of a microprocessor, etc. Exploiting the theory put forward by the paper, we highlight how these processes could be generated by suitably designed 2-d chaotic maps and how their second- and third-order spectra may be obtained and interpreted when exponentially or polynomially decaying distributions are assumed for mode sojourn times
Chaotic complex spreading sequences for asynchronous DS-CDMA-Part I: System modeling and results
Full text linkAbstract— This paper and its companion are devoted to the
evaluation of the impact of chaos-based techniques on communi-
cations systems with asynchronous code division multiple access.
Sequences obtained by repeating a truncated and quantized
chaotic time series are compared with classical -sequences and
Gold sequences by means of a performance index taken from
communication theory which is here defined and thoroughly dis-
cussed. This analysis reveals that, unlike conventional sequences,
chaotic spreading codes can be generated for any number of users
and allocated bandwidth. Numerical simulations are reported,
showing that systems based on chaotic spreading sequences per-
form generally better than the conventional ones. Some analytical
tools easing the comprehension of these advantages are here
summarized and proved in Part II where formal arguments are
developed and discussed to ensure general applicability of chaotic
spreading codes
On the Ultimate Limits of Chaos-Based Asynchronous DS-CDMA - Part I: Basic Definitions and Results
No full textThe ultimate limits of chaos-based asynchronous
direct-sequence code-division multiple access systems are investigated using the concept of capacity taken from information
theory. To this aim, we model the spreading at the transmitter
and the sampling of the incoming signal at the receiver with a
unique linear multi-input multi-output transfer function.We then
assume the existence of a coding/decoding pair that is able to
transmit information through this channel with a vanishing error
probability. The capacity of the system is then identified with
the maximum rate at which such an errorless link may operate.
The capacity is a random quantity depending on the spreading
sequences and, due to the asynchronism, on the users relative
delays and phases.We then compare different spreading strategies
[classical m and Gold codes, independent identically distributed
(i.i.d.) and chaos-based codes] in terms of expected performance
as well as of the probability that one method outperforms another.
To ease further analytical investigations that should cope with
expectations of logarithms, we measure capacity not only in bits
per use but also in codewords per use. Some formal results along
with extensive numerical evidence show that this does not alter
the performance ranking. Such a ranking shows that chaos-based
spreading always outperforms i.i.d. spreading and those trying
to mimic it. This aligns with and complements what was already
known about the ability of chaos-based techniques of minimizing
multiple access interference
Capacity of chaos-based asynchronous DS-CDMA systems with exponentially vanishing autocorrelations
No full textA receiver for synchronous DS-CDMA systems is proposed with a decision window that is aligned to encompass two half bits of each user. Such a receiver is compared with the classical one in terms of Shannon capacity showing a definite improvement, Based on this, traditional upper bounds and optimality criteria on the capacity of synchronous DS-CDMA systems are revised
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