In this paper Li–Yorke chaotic sets generated by shift and weighted shift maps are studied. The characterization of Li–Yorke chaotic sets by p-scrambled sets, maximal scrambled sets and orbit invariants are proved for the general shift maps. For weighted shift maps on infinite-dimensional spaces, the necessary and sufficient conditions for Li–Yorke chaotic are proved both in the abstract sequen...

It has been well-known that tight relationship exists between chaos and cryptography [Brown & Chua, 1996]. Many fundamental characteristics of chaos, such as ergodicity, mixing property and sensitivity to initial conditions/control parameters [Hao, 1993], can be connected with some cryptographic properties of good ciphers, such as confusion/diffusion, balance and avalanche property [Schneier, 1...

It is well known that most conventional control methods and many special techniques can be used for chaos control [Chen & Dong, 1998] whether the purpose is to reduce “bad” chaos or to introduce “good” chaos. Numerous control methodologies have been proposed, developed, tested and applied. Due to its great potential in nontraditional applications such as those found within the context of physic...

An approach is proposed for making chaotic a given stable Takagi–Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mec...

In this paper, a mathematical analysis of a possible way to chaos (in the sense of Li and Yorke) for bounded piecewise smooth systems of dimension three submitted to nonsmooth transitions is proposed. This study is based on period doubling method applied to the relied Poincaré map defined on a Poincaré section chosen in the neighborhood of the bifurcation point and transverse to the switching m...

A new mathematical concept of abstract similarity is introduced and illustrated in the space infinite strings on a finite number symbols. The problem chaos presence for Sierpinski fractals, Koch curve, as well Cantor set solved by considering natural map. This accomplished Poincaré, Li-Yorke Devaney chaos, including multi-dimensional cases. Original numerical simula...

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...