since the pioneering work of zadeh, fuzzy set theory has been applied to amyriad of areas. song and chissom introduced the concept of fuzzy time series andapplied some methods to the enrolments of the university of alabama. thereafter weapply fuzzy techniques for system identification and apply statistical techniques tomodelling system. an automatic methodology framework that combines fuzzytech...

A nonlinear chattering-free sliding mode control method is designed to stabilize fractional chaotic systems with model uncertainties and external disturbances. The main feature of this controller is rapid convergence to equilibrium point, minimize chattering and resistance against uncertainties. The frequency distributed model is used to prove the stability of the controlled system based on dir...

Although many mathematicians have searched on the fractional calculus since many years ago, but its application in engineering, especially in modeling and control, does not have many antecedents. Since there are much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. This paper deals with time-domain id...

In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of proposed method is proved by Barbalate’s lemma. Numeri...

The passage of light or of electrons through a disordered medium is modified in the presence of resonances. We describe a simple model for this problem, and present first results.

This paper introduces multifractal theory into the research of chaotic channels, and a novel model of chaotic channel is established from nonlinear science standpoint. By studying the relationship between multifractal dimensions and work environments, increments probability distribution, and statistical self-similarity of low power line communication (L-PLC) channel which is a typical chaotic c...

Among most machine learning algorithms for optimization problem including meta-heuristic search algorithms, the solution is drawn like a moth to a flame and cannot keep away. The track of chaotic variable can travel ergodically over the whole search space. In general, the chaotic variable has special characters, i.e., ergodicity, pseudo-randomness and irregularity. To enrich the searching behav...

In this paper, we explain why the chaotic model (CM) of Bahi and Michel (2008) accurately simulates gene mutations over time. First, we demonstrate that the CM model is a truly chaotic one, as defined by Devaney. Then, we show that mutations occurring in gene mutations have the same chaotic dynamic, thus making the use of chaotic models relevant for genome evolution.