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...

The control method of Ott, Grebogi, and Yorke (OGY) is used to stabilize the unstable periodic orbits of a chaotic relay system. Small variations in the height of the relay output are used as control input. The influence of the control activation bound is studied in detail via the one-dimensional Poincare map of the controlled system. The reduced sensitivity of the multi-step OGY method for hig...

Let f : X → be a self homeomorphism of continuum X, we show that the topological entropy induced system (2X, 2f) is infinite provided X\Ω(f) not empty. If furthermore regular curve then it shown has if and only Moreover prove for (C(X), C(f)) equivalence between following properties: (i) zero entropy; (ii) there no Li-Yorke pair (iii) any periodic subcontinnum A connected component C X\Ω(f), ⊂ ...

Recurrence Quantification Analysis (RQA) is a method for measuring the complexity of dynamical systems. determinism fundamental characteristic RQA, closely related to correlation sum. In this paper, we study asymptotic behavior these quantities interval maps. We show which cases sum exists. An example an map with zero entropy and point finite [Formula: see text]-limit set does not exist given. ...

Let $$f:X\rightarrow X$$ be a hereditarily locally connected continuum homeomorphism and denote respectively by P(f), AP(f) $$\Omega (f)$$ , the sets of periodic points, almost points non-wandering f. We show that any $$\omega $$ -limit set (resp. $$\alpha set) is minimal. Moreover, we (f)=AP(f)$$ . also prove if $$P(f)=\emptyset then there exists unique minimal set. On other hand, $$P(f)\ne \e...

The control method of Ott, Grebogi, and Yorke (OGY) is used to stabilize the unstable periodic orbits of a chaotic relay system. Small variations in the height of the relay output are used as control input. The influence of the control activation bound is studied in detail via the one-dimensional Poincaré map of the controlled system. The reduced sensitivity of the multi-step OGY method for hig...

In this paper, the authors investigate the anti-synchronization of chaotic Pan, Lorenz, and Lu systems and anti-synchronization of Liu and Cai systems. Global exponential synchronization of Pan, Lorenz, Lu, Liu, and Cai chaotic systems are established by using Lyapunov stability theory. Numerical simulations are performed to illustrate the effectiveness of the proposed synchronization schemes f...

This paper introduces the concept of Kato chaos to linear dynamics and its induced dynamics. investigates some properties for a continuous operator T operators T¯. The main conclusions are as follows: (1) If is accessible, then collection vectors whose orbit has subsequence converging zero residual set. (2) For defined on Fréchet space, equivalent dense Li–Yorke chaos. (3) preserved under itera...