Abstract
In this paper, we consider a special, but important class of one-dimensional coupled map lattices, namely, in which the local dynamics including logistic map as a prototype possesses a snap-back repeller. For smaller coupling strengths, the existence of Li–Yorke scrambled set is proved.
Highlights
In spatially extended systems, spatiotemporal chaos, as a complex dynamical phenomenon, appears in a broad area of natural phenomena [1,2,3,4,5,6,7,8,9,10]
We focus on the temporal chaos of a general form of one-dimensional map lattices (OML): Xn+1 = H(μ, e, Xn), where
The purpose of the present paper is to prove the following result: Theorem 1.1 If (H) is satisfied, there exists an e∗ 0 such that for any (μ, e) ∈ [μ∗, μ∗] × [–e∗, e∗], problem (1.1) is chaotic
Summary
Spatiotemporal chaos, as a complex dynamical phenomenon, appears in a broad area of natural phenomena [1,2,3,4,5,6,7,8,9,10]. The purpose of the present paper is to prove the following result: Theorem 1.1 If (H) is satisfied, there exists an e∗ 0 such that for any (μ, e) ∈ [μ∗, μ∗] × [–e∗, e∗], problem (1.1) is chaotic.
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