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In this paper we study some chaotic properties of the following systems which is posed by Kaneko in (Phys Rev Lett, 65: 1391-1394, 1990) and is related to the Belusov-Zhabotinskii reaction: $$\begin{aligned} u_{b}^{a+1}=(1-\alpha )r(u_{b}^{a})+ \frac{1}{2}\alpha [r(u_{b-1}^{a})+r(u_{b+1}^{a})], \end{aligned}$$where a is discrete time index, b is lattice side index with system size T, \(\alpha \in [0, 1]\) is coupling constant and r is a continuous selfmap on \(J=[0, 1]\). It is proven that for each continuous selfmap r on J, the topological entropy of such a coupled lattice system with \(\alpha =0\) is not less than the topological entropy of r, and that for each continuous selfmap on J with positive topological entropy, the above system with \(\alpha =0\) is \({\mathscr {P}}\)-chaotic, where \({\mathscr {P}}\) is one of the three properties: Li–Yorke chaos, distributional chaos, \(\omega \)-chaos. Moreover, we deduce that for each continuous selfmap r on J and any \(\alpha \in [0, 1]\), if r is \(\omega \)-chaotic, then so is the above system. Keywords Coupled map lattice \({\mathscr {P}}\)-chaos Topological entropy Mathematics Subject Classification 54H20 58F03 47A16 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (27) References1.R.L. Adler, A.G. Konheim, M.H. McAndrew, Topological entropy. Trans. Amer. Math. Soc. 309–319 (1965)2.L.S. Block, W.A. Coppel, Dynamics in One Dimension, Springer Monographs in Mathematics (Springer, Berlin, 1992)3.R. Bowen, Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. 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Applications in Chemistry Keywords Coupled map lattice $${\mathscr {P}}$$ P -chaos Topological entropy 54H20 58F03 47A16 Industry Sectors IT & Software Oil, Gas & Geosciences Telecommunications Authors Risong Li (1) Jianjun Wang (2) Tianxiu Lu (3) Ru Jiang (1) Author Affiliations 1. School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People’s Republic of China 2. Department of Mathematics, Sichuan Agricultural University, Yaan, Sichuan, 625014, People’s Republic of China 3. Department of Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, People’s Republic of China Continue reading... To view the rest of this content please follow the download PDF link above.