Turbulence, Erratic Property and Horseshoes in a Coupled Lattice System related with Belusov−Zhabotinsky Reaction

Document Type : Research Paper

Authors

School of Mathematic and Computer Science, Guangdong Ocean University Zhanjiang, Guangdong, P. R. China

Abstract

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.

Keywords

References

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Iranian Journal of Mathematical Chemistry
Volume 11, Issue 3
September 2020
Pages 133-140

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