No abstract

In this paper, traveling waves are analytically found in weakly coupling CML, with both global and neighbor couplings. The waves are triggered by the individual dynamics of the oscillators belonging to CML: saddle-node bifurcation cascades. Depending on the wave period different results are obtained, since the larger the period, the larger the collapse produced in the boxes of saddle-node bifurcation cascades.

Starting from the cycle permutation σ 2 k associated with the 2 k -periodic orbit of the period doubling cascade we obtain the inverse permutation σ −1 2 k . Then we build a matrix permutation related to σ −1 2 k , which includes the visiting order of the 2 k -periodic orbit points.After some manipulations a recurrence relation of matricial representation of period doubling cascade is obtained. Finally the explicit matricial representation is reached.