Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices

In this paper, we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices. We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small. That is,where $x_i(n)$ correspond to the coordinates of $m$ nodes at the iterative step $n$. Moreover, when the uncoupled system is generated by the tent map and the lattice consists of two nodes, we prove a phase transition occurs between synchronization and intermittent behaviors. That is, $$lim_{nrightarrow infty}| x_1(n)-x_2(n)|=0quadtext{for } Big|c-frac12Big|frac14$, where $0le cle 1$ is the coupling.