Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices (Analysis in Theory and Applications, 2021)
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_{n→ ∞}| x_1(n)-x_2(n)|=0\quad\text{for }\ \ \Big|c-\frac12\Big|\frac14$, where $0\le c\le 1$ is the coupling.