In this paper we provide an extension of the classical Chaos game for IFSP. The paper is divided into two parts: in the first one, we discuss how to determine the integral with respect to a measure which is a combination of a self-similar measure from an IFSP along with a density given by an IFSM. In the second part, we prove a version of the Ergodic Theorem for the integration of a continuous ...

For a Poisson point process X , Itô’s famous chaos expansion implies that every square integrable regression function r with covariate X can be decomposed as a sum of multiple stochastic integrals called chaos. In this paper, we consider the case where r can be decomposed as a sum of δ chaos. In the spirit of Cadre and Truquet (2015), we introduce a semiparametric estimate of r based on i.i.d. ...

This paper proposes a private communication system with chaos using fixed-point digital computation. When fixed-point computation is adopted, chaotic properties of the modulated signal should be checked carefully as well as calculation error problems (especially, overflow problems). In this paper, we propose a novel chaos modem system for private communications including a chaotic neuron type n...

A model for a chaotic micro-oscillator is developed by adding a new control system to an electrostatic actuator consisting of two electrodes: the substrate and a cantilever beam on top. The electrostatic actuator itself has a single stable equilibrium over a range of voltage, whereas adding the controller, which has a quadratic function, creates a voltage range for bistability. The bi-stability...

This paper discusses a circuit family including a dependent switched capacitor (DSC). The DSC function is instantaneously short of one capacitor at the moment when its voltage reaches a threshold. The chaos generation can be guaranteed theoretically, We also consider a master-slave system. If there does not exist a homoclinic orbit in the master chaos attractor, it exhibits either in-phase or i...

This paper presents a new procedure of generating hash functions which can be evaluated using some mathematical tools. This procedure is based on discrete chaotic iterations. First, it is mathematically proven, that these discrete chaotic iterations can be considered as a particular case of topological chaos. Then, the process of generating hash function based on the topological chaos is detail...

This research deals with the initial investigations on the concept of a chaos-driven evolutionary algorithm Differential evolution. This paper is aimed at the embedding of simple twodimensional chaotic system, which is Lozi map, in the form of chaos pseudo random number generator for Differential Evolution. The chaotic system of interest is the discrete dissipative system. Repeated simulations ...

A new proposal to have secure communications in a system is reported. The basis is the use of a synchronized digital chaotic systems, sending the information signal added to an initial chaos. The received signal is analyzed by another chaos generator located at the receiver and, by a logic boolean function of the chaotic and the received signals, the original information is recovered. One of th...

To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization ...

A probabilistic approach which exploits the domain and distribution of the uncertain model parameters has been developed for the design of robust input shapers. A Polynomial Chaos based expansion approach is used to approximate uncertain system states and cost functions in terms of finite-dimensional series expansion in the stochastic space. Residual energy of the system is used as cost functio...