In this paper, the dynamics of elementary cellular automaton (ECA) rule 73 is investigated under the framework of the bi-infinite symbolic sequence space. This paper provides a rigorous mathematical analysis for the evolution of symbol sequences in some subsystems of rule 73. ECA rule 73, a member of Wolfram’s class III and Chua’s complex Bernoulli-shift rules, defines many more subsystems with...

Given K real d-by-d nonsingular matrices S 1, . . . , S K , by extending the well-known Li-Yorke chaotic description of a deterministic nonlinear dynamical system, to a discrete-time linear inclusion/control dynamical system xn ∈ {S 1, . . . , S K} xn−1, x0 ∈ R d and n ≥ 1, we study the irregularity of orbit (xn(x0, σ))n≥1, governed by the law σ : N → {1, . . . , K}, for any initial state x0 ∈ ...

In this paper, a chaotic three dimansional dynamical system is proposed, that modification of the in Volos et al. (2017). The new has two hyperbolic sine nonlinear terms, as opposed to original only included one, order optimize system’s behavior, which confirmed by calculation maximal Lyapunov exponents and Kaplan-Yorke dimension. experimentally realized, using Bi-color LEDs emulate functions. ...

In this paper, the parameter-switching technique was applied to control chaos in Chen oscillator and as a decryption mechanism secure transmission system, transmit RGB grayscale images. past few decades, considerable efforts have been put into study of stabilization chaotic dynamical systems. Most well-known methods, such Ott, Grebogi, Yorke (OGY), Pyragas, open-loop force an unstable periodic ...

In this paper, the problems on chaos control and synchronization of Li chaotic systems with unknown parameters are considered. Firstly, the Li chaotic systems are introduced. Secondly, the adaptive control system with only two state feedbacks for synchronization of the Li chaotic systems is presented and the parameter identification method is also given. Sufficient conditions for the stability ...

Chaotic dynamical systems characteristically exhibit erratic, seemingly random, behavior. They are highly sensitive to initial conditions. Any alteration to the state of a chaotic system will eventually lead to very large differences in behavior. Until recently, the preferred approach to chaotic dynamical systems has been to avoid them. A method developed by Ott, Grebogi, and Yorke (OGY) takes ...

The seminal papers by Pecora and Carrol (PC) [1] and Ott, Grebogi and Yorke (OGY) [2] in 1990 have induced avalanche of research works in the field of chaos control. Chaos synchronization in dynamical systems is one of methods of controling chaos, see, e.g. [1-8] and references therein.The interest to chaos synchronization in part is due to the application of this phenomenen in secure communica...

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...