(untitled) (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, _n→ ∞| x_1(n)-x_2(n)|=0for |c-12|14, where 0c1 is the coupling.