In the past decade, there have been some studies about control methods with the purpose of either reducing “bad” chaos or introducing “good” chaos [Chen & Dong, 1998]. Due to its great potential in nontraditional applications such as those found within the context of physical, chemical, mechanical, electrical, optical, and particularly, biological and medical systems [Chen et al., 2001; Schiff ...

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

We investigate the prevalence of Li-Yorke pairs for C and C multimodal maps f with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If f is topologically mixing and has no Cantor attractor, then typical (...

This paper proposes a method to construct one-dimensional discrete chaotic system. First, we define generalized distance function control the boundedness of Based on Marotto’s theorem, systems are proven be in sense Li–Yorke, and corresponding chaos criterion theorem is proposed. The system can distributed uniformly by adjusting parameters. In this paper, propose an image encryption scheme base...

A homeomorphism f : X → X of a compactum X is expansive (resp. continuum-wise expansive) if there is c > 0 such that if x, y ∈ X and x 6= y (resp. if A is a nondegenerate subcontinuum of X), then there is n ∈ Z such that d(f(x), f(y)) > c (resp. diam f(A) > c). We prove the following theorem: If f is a continuum-wise expansive homeomorphism of a compactum X and the covering dimension of X is po...

An approach is proposed for making a given stable continuous-time Takagi-Sugeno (TS) fuzzy-system chaotic, by first discretizing it and then 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 posit...