Chaotic signals have been considered potentially attractive in many signal processing applications ranging from wideband communication systems to cryptography and watermarking. Besides, some devices as nonlinear adaptive filters and phase-locked loops can present chaotic behavior. In this paper, we derive analytical expressions for the autocorrelation sequence, power spectral density and essent...

By using dissipative system Lagrange equation, the strongly nonlinear dynamic equation of torsional vibration system is deduced, which contains a class of square and cube nonlinear rigidity and combination harmonic excitations. Bifurcation characteristics of the strongly nonlinear system are analyzed in the autonomous and non-autonomous situations by means of singular point stability theory and...

We consider a family of chaotic skew tent maps. The skew tent map is a two-parameter, piecewise-linear, weakly-unimodal, map of the interval Fa;b. We show that Fa;b is Markov for a dense set of parameters in the chaotic region, and we exactly nd the probability density function (pdf), for any of these maps. It is well known, [1], that when a sequence of transformations has a uniform limit F , a...

In switched dynamic system the continuous phase ow is accompanied by a stream of switching events. If the system exhibits chaotic behavior this event stream can be used for generating a rectangular wave with chaotic switching times. In this paper the probability distribution of the intervals between the switching times is derived. Two system di erent in their continuous state model are treated:...

The recently developed short-time linear response algorithm, which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation, yields high precision of the response prediction. However, the computation of the shorttime linear response formula with the full rank tangent map can be expensive. Here we propose a numerical method to potentially overcome the...

In this paper, statistical analysis of watermarking schemes based on correlation detection is presented. Statistical properties of watermark sequences generated by piecewise-linear Markov maps are exploited, resulting in superior watermark detection reliability. Correlation/spectral properties of such sequences are easily controllable, a fact that affects the watermarking system performance. A ...

This paper provides algorithms in order to solve an interval implicit function of the Poincaré map generated by a continuous piecewise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MAT LAB and INT LAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear...

and Applied Analysis 3 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 −1.5 −1 −0.5 0 0.5 1 1.5 x1 x 2 Figure 1: Phase portrait of the chaotic YangHenon map system with a1 1.4, b1 0.3. where a1 1.4, b1 0.3 and positive argument n1 0, 1, 2, 3, . . . , n. The Yang chaotic behaviors of Henon map system are quoted 19 by phase portraits in Figure 1. The Henon map system is invertible if b1 / 0. The inversed H...