جستجوی مقالات مرتبط با کلیدواژه « coupled map lattice » در نشریات گروه « شیمی »

In this paper‎, ‎the chaotic properties of‎ ‎the following Belusov-Zhabotinskii's reaction model is explored:‎ ‎alk+1=(1-η)θ(‎alk)+(1/2) η[θ(‎al-1k)-θ(al+1k)], where k is discrete‎ ‎time index‎, ‎l is lattice side index with system size M‎, η∊ ‎[0‎, ‎1) is coupling constant and $theta$ is a continuous map on‎ ‎W=[-1‎, ‎1]. This kind of system is a generalization of the chemical‎ ‎reaction model which was presented by García Guirao and Lampart‎ ‎in [Chaos of a coupled lattice system related with the Belusov–Zhabotinskii reaction, J. Math. Chem. ‎48 (2010) 159-164] and stated by Kaneko in [Globally coupled chaos violates the law of large numbers but not the central-limit theorem, Phys. Rev.‎ ‎Lett‎. ‎65‎ (1990) ‎1391-1394]‎, ‎and it is closely related to the‎ ‎Belusov-Zhabotinskii's reaction‎. ‎In particular‎, ‎it is shown that for‎ ‎any coupling constant η ∊ [0‎, ‎1/2)‎, ‎any‎ ‎r ∊ {1‎, ‎2‎, ...} and θ=Qr‎, ‎the topological entropy‎ ‎of this system is greater than or equal to rlog(2-2η)‎, ‎and‎ ‎that this system is Li-Yorke chaotic and distributionally chaotic,‎ ‎where the map Q is defined by‎ ‎Q(a)=1-|1-2a|‎, ‎ a ∊ [0‎, ‎1], and Q(a)=-Q(-a),‎ a ∊ [-1‎, ‎0]. Moreover‎, ‎we also show that for any c‎, ‎d with‎ ‎0≤c≤ d≤ 1, ‎η=0 and θ=Q‎, ‎this system is‎ ‎distributionally (c‎, ‎d)-chaotic.‎

In this paper we continue to study the chaotic properties of the following lattice dynamical system: bji+1= a1 g(bji)+ a2 g(bj-1i)+ a3 g(bj+1i), where i is discrete time index, j is lattice side index with system size L, g is a selfmap on [0, 1] and a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1 are coupling constants. In particular, it is shown that if g is turbulent (resp. erratic) then so is the above system, and that if there exists a g-connected family G with respect to disjointed compact subsets D1, D2, …, Dm, then there is a compact invariant set K'⊆D' such that F |K' is semi-conjugate to m-shift for any coupling constants a1+a2+a3 ∊ [0, 1] with  a1+a2+a3=1, where D' ⊆ IL is nonempty and compact. Moreover, an example and two problems are given.

In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itself is said to be P-chaotic if it has the pseudo-orbit-tracing property and the closure of the set of all periodic points for $Theta$ is the space $Z$. Also, an example and three open problems are presented.

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