We first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions i.e., a highdimensional discrete dynamical system . Then, the recent 0-1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. ...

Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also s...

This paper is concerned with chaos induced by regular snap-back repellers. One new criterion of chaos induced by strictly coupled-expanding maps in compact sets of metric spaces is established. By employing this criterion, the nondegenerateness assumption in the Marotto theorem established in 1978 is weakened. In addition, it is proved that a regular snap-back repeller and a regular homoclinic ...