@article {
author = {Wang, Hongqing and Li, Risong},
title = {Topological Entropy, Distributional Chaos and the Principal Measure of a Class of Belusov−Zhabotinskii's Reaction Models Presented by García Guirao and Lampart },
journal = {Iranian Journal of Mathematical Chemistry},
volume = {12},
number = {1},
pages = {57-65},
year = {2021},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2021.240450.1541},
abstract = {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.},
keywords = {Coupled map lattice,Distributional chaos,Principal measure,Chaos in the sense of Li-Yorke,Topological entropy},
url = {https://ijmc.kashanu.ac.ir/article_111347.html},
eprint = {https://ijmc.kashanu.ac.ir/article_111347_ed4c4ec73afdcc653e1ef92fced8e5ab.pdf}
}