Intermittent behaviors in weakly coupled map lattices

In this paper, we study intermittent behaviors of coupled piecewise-expanding map lattices with two nodes and a weak coupling. We show that the successive phase transition between ordered and disordered phases occurs for almost every orbit. That is, we prove ${\mathrm{lim\hspace{0.17em}inf}}_{n\to \mathrm{\infty }}\mathrm{\mid }{x}_1(n)-x_2(n)\mathrm{\mid }=0$ and ${\mathrm{lim\hspace{0.17em}sup}}_{n\to \mathrm{\infty }}\mathrm{\mid }{x}_1(n)-x_2(n)\mathrm{\mid }\ge c_0>0$, where $x_1(n), x_2(n)$correspondtothecoordinatesoftwonodesattheiterativestep$n$. We also prove the same conclusion for weakly coupled tent-map lattices with any multi-nodes.