In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.

A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the heavy-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.

We investigate the statistical features of both random- and chaos-based FM timing signals to ascertain their applicability to digital circuits and systems. To achieve such a goal, we consider both the case of single- and two-phase logic and characterize the random variable representing, respectively, the time lag between two subsequent rising edges or between two consecutive zero-crossing points of the modulated timing signal. In particular, we determine its probability density and compute its mean value and variance for cases which are relevant for reducing Electromagnetic emissions. Finally, we address the possible problems of performance degradation in a digital system driven by a modulated timing signal and to cope with this we give some guidelines for the proper choice of the statistical properties of the modulating signals.

The problem of aggregating different stochastic process into a unique one that must be characterized based on the statistical knowledge of its components is a key point in the modeling of many complex phenomena such as the merging of traffic flows at network nodes. Depending on the physical intuition on the interaction between the processes, many different aggregation policies can be devised, from averaging to taking the maximum in each time slot. We here address flows averaging and maximum since they are very common modeling options. Then we give a set of axioms defining a general aggregation operator and, based on some advanced results of functional analysis, we investigate how the decay of correlation of the original processes affect the decay of correlation (and thus the self-similar features) of the aggregated process.

Synchronization 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. 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].

We 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.

Though considerable effort has recently been devoted to hardware realization of one-dimensional chaotic systems, the influence of implementation inaccuracies is often underestimated and limited to non-idealities in the non-linear map. Here we investigate the consequences of sample-and-hold errors. Two degrees of freedom in the design space are considered: the choice of the map and the sample-and-hold architecture. Current-mode systems based on Bernoulli Shift, on Tent Map and on Tailed Tent Map are taken into account and coupled with an order-one model of sample-and-hold to ascertain error causes and suggest implementation improvements.

The reduction of undesired electromagnetic emissions in switched power converters is a hot topic. Here, we propose a chaos based methodology to synthesize PWM-like signals for controlling the drives of induction motors. This approach reduces drastically the interference due to the drive-motor ensemble, and does not significantly alter the motor performance. The benefit is a 20 dB reduction in the peak of the emitted power density spectrum. This result is herein confirmed three times: first with an analytical approach based on approximations whose impact is progressively reduced; then by means of simulation; finally by laboratory testing of a working prototype.

The aim of this contribution is to take a further step in the study of the impact of chaos-based techniques on classical DS-CDMA systems. The problem addressed here is the sequence phase acquisition and tracking which is needed to synchronize the spreading and despreading sequences of each link. An acquisition mechanism is considered and analyzed in depth to identify analytical expressions of suitable system performance parameters, namely outage probability, link startup delay and expected time to service. Special chaotic maps are considered to show that the choice of spreading sequences can be optimized to accelerate and improve the spreading codes acquisition phase.