turbulence, erratic property and horseshoes in a coupled lattice system related with belusov−zhabotinsky reaction

In this paper we continue to study the chaotic properties of the following lattice dynamical system: bji+1= a1 g(bji)+ a2 g(bj1i)+ 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 gconnected 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 semiconjugate to mshift 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.