Abstract
In this paper, fuzzy mapping is selected to study the coupled system in non-autonomous systems. The following conclusions are obtained: (1) The fuzzy system (F(X),{f˜n}n=1∞) is P1-chaos, then the coupled system (1–3) is P1 chaos. Where P1-chaos is one of the followings: (F1,F2)-Chaos, Li–Yorke chaos, distributional chaos, spatio-temporal chaos, densely δ-chaos, densely chaos, Ruelle-Takens chaos, Kato’s chaos. (2) The fuzzy system (F(X),{f˜n}n=1∞) is P2- sensitive, then the coupled system (1–3) is P2-sensitive. Where P2-sensitive is one of the followings: sensitive, Li–Yorke sensitive, densely Li–Yorke sensitive, infinitely sensitive, syndetically sensitive, cofinitely sensitive, F-sensitive, (F1,F2)-sensitive. (3) The fuzzy system (F(X),{f˜n}n=1∞) is transitive, exactness or accessible, then the coupled system (1–3) is transitive, exactness or accessible.
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