Resonance effect of direction-phase clusters in a scale-free network

It is known that for chaotic flows, a weak coupling does not always make the coupled systems approach synchronization but sometimes makes them become more complicated (Phys. Rev. E, 67 (2003) 045203(R)). We here report that a similar situation also occurs in the coupled chaotic maps, where a weak coupling will make the number of direction-phase clusters N_c increase. We find a double-resonance effect on the coupling strength ε, where the first resonance comes from the coupling-induced periodic behaviors and the second one is due to the disappearance of the disorder phase. The mechanism of the second resonance is revealed through the out-of-phase links. Moreover, we show that the critical coupling ε_c of the maximum N_c will increase rapidly with the bifurcation parameter μ but slowly with the range of the distribution of non-identical oscillators.