The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +∞) being granted by the study performed in [9], the aim of the present paper is to prove the resulting functional central limit theorem. It involves the study of a measure-valued process describing the fluctuations (at scale n) of the em...

A new scheme for generating good pseudo-random numbers, based on the composition of chaotic maps, is studied. In this method, hereafter called the chaotic stream cipher, one first uses a known chaotic dynamical system to generate a sequence of pseudo-random bytes, then applies certain permutations to them, using the discretized version of another two-dimensional chaotic map. Standard statistica...

We describe a high-speed physical random number generator based on a hybrid Boolean network with autonomous and clocked logic gates, realized on a reconfigurable chip. The autonomous logic gates are arranged in a bidirectional ring topology and generate broadband chaos. The clocked logic gates receive input from the autonomous logic gates so that random numbers are generated physically that pas...

One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is use least significant bits or digits finite-precision numbers defined by chaotic orbits. In this study, we show that results obtained using such an approach are very prone rounding errors and discretization effects. Thus, it appears generated close random even when parameters correspond non-chaotic os...

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....

The Creation of the Universe is a theme that inspired artists and musicians throughout ages. However, it was not only idea creation aroused interest these artists, but also existence Chaos, which believed to have preceded act creation. In France Louis XIV, arts music were profoundly influenced by Classical Antiquity, as proven artworks this era. Artists composers sought depict Universe, often r...

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...

today we are facing with a turbulent world full of complexity and change. contemporary problems are too complicated for rational, logical solutions. they admit insights, not answers. chaos theory is a solution to reveal insights into the structure and the dynamics of complex systems. chaos theory is in formative stage, but we can use it in management practices. this article is about application...

This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment. In fast growing world, real life situations are characterized by their behaviors and processes. The chaos variables defined to study such type of problems. Classical mathematics deals with numbers as static less value-added, while it dynamic evolutionary, comparatively more value-add...