文献类型：期刊文献

英文题名：Topological Entropy, Distributional Chaos and the Principal Measure of a Class of Belusov-Zhabotinskii's Reaction Models Presented by Garcia Guirao and Lampart

作者：Wang, Hongqing[1];Li, Risong[1]

机构：[1]Guangdong Ocean Univ, Sch Math & Comp Sci, Zhanjiang 524025, Guangdong, Peoples R China

年份：2021

卷号：12

期号：1

起止页码：57

外文期刊名：IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY

收录：ESCI(收录号：WOS:000647135700004)、WOS

基金：This work was supported by the National Natural Science Foundation of China (no. 11501391), Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province (2018RZJ03), Opening Project of Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province (2018QZJ03), Ministry of Education Science and Technology Development center (2020QT13), the Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things (2020WZJ01) and Scientific Research Project of Sichuan University of Science and Engineering (2020RC24).

语种：英文

外文关键词：Coupled map lattice; Distributional chaos; Principal measure; Chaos in the sense of Li-Yorke; Topological entropy

外文摘要：In this paper, the chaotic properties of the following Belusov-Zhabotinskii's reaction model is explored: a(1)(k+1) = (1-eta)theta(a(1)(k))+1/2 eta[theta(a(1-1)(k)) - theta(a(1+1)(k))]. where k is discrete time index, l is lattice side index with system size, eta is an element of[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 Garcia 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 eta is an element of [0,1/2], any r is an element of{1,2,...} and theta=Q(r), the topological entropy of this system is greater than or equal to rlog(2-2 eta), and that this system is Li-Yorke chaotic and distributionally chaotic, where the map Q is defined by Q(a) = 1 - vertical bar 1-2a vertical bar a is an element of[0,1] and Q(a) = -Q(-a), a is an element of[-1,0]. Moreover, we also show that for any c,d with 0 <= c <= d <= 1, eta = 0 and theta = Q, this system is distributionally (c,d)-chaotic. (C) 2021 University of Kashan Press. All rights reserved