From decimal expansion of real numbers to complex behaviour in physical, biological and human-made systems, deterministic chaos is ubiquitous. One the simplest examples a nonlinear dynamical system that exhibits well known 1-dimensional piecewise linear Tent map. The map (and their skewed cousins) are instances larger family maps namely Generalized Luröth Series (GLS) which studied for rich num...

It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method MVM . It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exac...

We propose the deep-zoom analysis of composition logistic map and tent map, which are well-known discrete one-dimensional chaotic maps. The technique transforms each point a given orbit by removing first k-digits after decimal separator. found that pseudo-random qualities as number generator (PRNG) improve k parameter increases. This was evidenced fact it successfully passed randomness tests ev...

The effect of noise on self-similar set is studied. The iteratie procedure used to generate the self-similar set is moidified by adding a stochastic variable to the diameter of generating sets at each iteration. The noise may causes the generating set to collapse to a point. Distribution functions are found describing the probability that any generating set collapse. The effect of chaotic distu...

This paper focuses on an interesting phenomena when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift map and their analogues, even in a highprecision floating-point arithmetic. Although the results cannot directly generalized to most chaotic systems, the risk...

Information security using chaotic dynamics is a novel topic in the wireless sensor network (WSN) research field. After surveying analog and digital chaotic security systems, we give a state of the art of chaotic S-Box design. The substitution tables are nonlinear maps that strengthen and enhance block crypto-systems. This paper deals with the design of new dynamic chaotic S-Boxes suitable for ...

Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic commun...

Secure exchange of sensitive information between different entities is a serious challenge in today’s environment. Therefore, various cryptosystems have been created specifically for this purpose. Various operations are used these cryptosystems. The most common substitution and permutation. substitution-box (S-box), look-up table that takes x bits as input replaces them with y bits, responsible...

We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form w...

We present an analog circuit implementation of the novel partial control method, that is able to sustain chaotic transient dynamics. The electronic circuit simulates the dynamics of the onedimensional slope-three tent map, for which the trajectories diverge to infinity for nearly all the initial conditions after behaving chaotically for a while. This is due to the existence of a nonattractive c...