In this paper we examine a very simple and elegant example of high-dimensional chaos in a coupled array of flows in ring architecture that is cyclically symmetric and can also be viewed as an N-dimensional spatially infinite labyrinth (a "hyperlabyrinth"). The scaling laws of the largest Lyapunov exponent, the Kaplan-Yorke dimension, and the metric entropy are investigated in the high-dimension...

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits (T ) of a dynamical system scales as a function of computer precision (ε) and the correlation dimension (d) of the chaotic attractor: T ∼ ε. In this work, we are concerned with increasing the average p...

Combinatorial techniques are applied to the symbolic dynamics representing transient chaotic behavior in tent maps in order to solve the problem of Ott-Grebogi-Yorke control to the nontrivial fixed point occurring in such maps. This approach allows "preimage overlap" to be treated exactly. Closed forms for both the probability of control being achieved and the average number of iterations to co...

Over the past decade, the problem of chaos controlling in plasmas attracted significant attention due to the importance of this topic for many processes in plasma physics [1-3]. In addition to the general interest of this subject the studies were motivated by the possibility of reduction of the anomalous transport, associated with plasma turbulent phenomena. It is well known that almost all sys...

Chaos occurs in the crystal growth process as an irregular swing phenomenon flexible shaft rotating-lifting (FSRL) system. may lead to failure of mono-silicon production. Therefore, it should be suppressed. Many chaos control methods have been proposed theoretically and some them used applications. For a practical plant displaying harmful chaos, engineers from specific area usually face with ch...

This paper studies cellular automata in two aspects: Ergodic and topological behavior. For ergodic aspect, the formulae of measure-theoretic entropy, topological entropy and topological pressure are given in closed forms and Parry measure is demonstrated to be an equilibrium measure for some potential function. For topological aspect, an example is examined to show that the exhibition of snap-b...

The paper analyzes the dynamic properties of the neoclassical one-sector growth model with di!erential savings in the sense of Kaldor}Pasinetti. The economy exhibits unstable steady states and #uctuations if the income distribution varies su$ciently and if shareholders save more than workers. The paper analyzes in detail the dynamics for the case with a "xed proportions technology as well as wi...

This paper is devoted to an in-depth study of cellular automaton rule 180 under the framework of symbolic dynamics. Rule 180, a member of Wolfram’s class IV and Chua’s hyper Bernoulli shift rules, defines infinite number of generalized sub-shifts. An effective method of constructing the shift invariant sets of the rule’s global map is proposed. It is noted that this method is also applicable to...

Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott}Grebogi}Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos con...

‎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...