文献类型：期刊文献

英文题名：Kato's Chaos and P-Chaos of a Coupled Lattice System given by Garcia Guirao and Lampart which is Related with Belusov-Zhabotinskii Reaction

作者：Li, Risong[1]

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

年份：2020

卷号：11

期号：1

起止页码：1

外文期刊名：IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY

收录：ESCI(收录号：WOS:000526179300001)、WOS

基金：The author is very grateful to the referees for their careful reading, comments, and suggestions, which help us improve this paper. This work was supported by the National Natural Science Foundation of China (Grant No. 11501391, 61573010), the Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province (2018RZJ03) and the Opening Project of Bridge Non-destruction Detecting and Engineering Computing Key Laboratory of Sichuan Province (2018QZJ03).

语种：英文

外文关键词：Coupled map lattice; Kato's chaos; P-chaos; Devaney's chaos; Li-Yorke's chaos; Tent map

外文摘要：In (J. Math. Chem., 48: 66-71, 2010) and (J. Math. Chem., 48: 159-164, 2010) Garcia Guirao and Lampart presented the following lattice dynamical system stated by Kaneko in (Phys Rev Lett, 65: 1391-1394, 1990) which is related to the Belusov-Zhabotinskii reaction: z(v)(u+1) = (1 - eta)Theta(z(v)(u)) + 1/2 eta[Theta(z(v-1)(u)) - Theta(z(v+1)(u))], where u is discrete time index, is lattice side index with system size M, eta is an element of [0,1] is coupling constant and Theta is a continuous selfmap on H. They proved that for the tent map Theta defined as Theta(z) = 1 - vertical bar 1-2z vertical bar for any z is an element of H, the above system with eta=0 has positive topological entropy and that such a system is Li-Yorke chaotic and Devaney chaotic. 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. (C) 2020 University of Kashan Press. All rights reserved