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. ...

We show that graph map with zero topological entropy is Li-Yorke chaotic if and only it has an NS-pair (a pair of non-separable points containing in a same solenoidal $\omega$-limit set), non-diagonal IN-pair IT-pair. This completes characterization sequence for maps.

This paper provides an easily verifiable sufficient condition for topological chaos for unimodal maps which can be satisfied when the well-known Li Yorke condition is not satisfied. It then shows how this result can be applied to a model of endogenous growth with externalities to establish the existence of chaotic equilibrium growth paths in that framework. Journal of Economic Literature Classi...