This paper gives an overview of the use of Polynomial Chaos expansions to represent stochastic processes in numerical simulations. Several methods are presented to perform arithmetic on, as well as to evaluate polynomial and non-polynomial functions of variables respresented with Polynomial Chaos expansions. These methods include Taylor series, a newly developed integration method as well as a ...

A probabilistic approach, which exploits the domain and distribution of the uncertain model parameters, has been developed for the design of robust input shapers. Polynomial chaos expansions are used to approximate uncertain system states and cost functions in the stochastic space. Residual energy of the system is used as the cost function to design robust input shapers for precise rest-to-rest...

This paper is devoted to the derivation of an exact analytical expression of the bit error rate for chaos-based DS-CDMA systems. For the studied transmission system, we suppose that synchronization is achieved perfectly, coherent reception is considered, and an Additive White Gaussian Noise channel (AWGN) is assumed. In the first part of the paper, performance of a mono-user system with differe...

This chapter provides an overview of the state of the art of current chaos communication schemes and introduces the use of signal processing to improve the communication performances. Popular communication schemes in the literature, including chaotic spreading sequence (CSS), chaotic carrier (CC), chaos masking (CM), chaos shift keying (CSK), differential chaos shift keying (DCSK) and chaotic p...

a sigmoid function is necessary for creation a chaotic neural network (cnn). in this paper, a new function for cnn is proposed that it can increase the speed of convergence. in the proposed method, we use a novel signal for controlling chaos. both the theory analysis and computer simulation results show that the performance of cnn can be improved remarkably by using our method. by means of this...

Corresponding Author: Thamizhchelvy, K. Faculty of Computing, Sathyabama University, Chennai, India Email: [email protected] Abstract: An Efficient Image Generation Algorithm is proposed. It generates Message Authentication Image (MAI) by using Fractals and chaos theory. The fractal images are generated by using Iterated Function System (IFS) techniques. We implemented and generated the f...

Background Recently, development of chaos theory brings up scientist into a new era in analyzing nonlinear systems. It is known that the chaos exhibits a deterministic random behavior. In particular, the OGY (OttGrebogi-Yorke) method drove the research of chaos control to nonlinear analyst. Yet it needs more investigation on such nonlinear systems in designing control algorithms. Recently, Vinc...

Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated....

We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factorK(τ, x, y,M), that depends on the number of open channelsM , a non-symmetry breaking parameter x, and a symmetry breaking parameter y. Several terms in the Taylor expansion about τ = 0, which depend on all ...