Information technology applications of statistical nonlinear dynamics
Gianluca Setti · 2008
Summary form only given. Recent developments have highlighted that a statistical approach may greatly benefit the study of discrete-time complex (chaotic) system (maps). In this case, in fact, critical dependence on initial condition, probably the widest known feature of chaotic behavior, prevents the study of single trajectories from giving information which are globally valid. On the contrary, a highly regular behaviour exists for the distribution of the points describing the evolution of a set of trajectories at each iteration step. We will formalize this approach by introducing a theoretical framework that is based on the classical Perron-Frobenius Operator (PFO), which accounts for the evolution of the probability densities describing the distribution of the system state variable at each iteration step. We then focus on Piecewise Affine Markov (PWAM) maps, and by specializing the set of theoretical tools that we have introduced, we will show how such maps can be considered as easily implementable, stochastic processes generators with tunable statistical features. Such a well-developed theoretical framework can be applied to several topics related to IT, such as Spreading sequence design for Direct Sequences Code Division, Multiple Access (DS-CDMA), EMI (Electro-Magnetic Interference) reduction, True random number generation.