TY - JOUR
ID - 110810
TI - Turbulence, Erratic Property and Horseshoes in a Coupled Lattice System related with Belusov−Zhabotinsky Reaction
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Zhao, Yu
AU - Li, Risong
AD - School of Mathematic and Computer Science, Guangdong Ocean University
Zhanjiang, Guangdong, P. R. China
AD - School of Mathematic and Computer Science, Guangdong Ocean University Zhanjiang, Guangdong, P. R. China
Y1 - 2020
PY - 2020
VL - 11
IS - 3
SP - 133
EP - 140
KW - Coupled map lattice
KW - Turbulence
KW - Erratic property
KW - Tent map
DO - 10.22052/ijmc.2020.160449.1413
N2 - In this paper we continue to study the chaotic properties of the following lattice dynamical system: bji+1= a1 g(bji)+ a2 g(bj-1i)+ a3 g(bj+1i), where i is discrete time index, j is lattice side index with system size L, g is a selfmap on [0, 1] and a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1 are coupling constants. In particular, it is shown that if g is turbulent (resp. erratic) then so is the above system, and that if there exists a g-connected family G with respect to disjointed compact subsets D1, D2, …, Dm, then there is a compact invariant set K'⊆D' such that F |K' is semi-conjugate to m-shift for any coupling constants a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1, where D' ⊆ IL is nonempty and compact. Moreover, an example and two problems are given.
UR - https://ijmc.kashanu.ac.ir/article_110810.html
L1 - https://ijmc.kashanu.ac.ir/article_110810_ef4de719dcba034b6498afbc94e028ce.pdf
ER -