University of KashanIranian Journal of Mathematical Chemistry2228-648912120210301Topological Entropy, Distributional Chaos and the Principal Measure of a Class of Belusov−Zhabotinskii's Reaction Models Presented by García Guirao and Lampart 576511134710.22052/ijmc.2021.240450.1541ENHongqingWangSchool of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, P. R. ChinaRisongLiSchool of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, P. R. ChinaJournal Article20210126In this paper, the chaotic properties of the following Belusov-Zhabotinskii's reaction model is explored: a<sub>l</sub><sup>k+1</sup>=(1-η)θ(a<sub>l</sub><sup>k</sup>)+(1/2) η[θ(a<sub>l-1</sub><sup>k</sup>)-θ(a<sub>l+1</sub><sup>k</sup>)], 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, <em>J. Math. Chem.</em> <strong></strong><strong>48</strong> (2010) 159-164] and stated by Kaneko in [Globally coupled chaos violates the law of large numbers but not the central-limit theorem, <em>Phys. Rev. Lett.</em> <strong>65</strong> (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=Q<sup>r</sup>, 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.https://ijmc.kashanu.ac.ir/article_111347_ed4c4ec73afdcc653e1ef92fced8e5ab.pdf