Non-universal dependence of spatiotemporal regularity on randomness in coupling connections

We investigate the spatiotemporal dynamics of a network of coupled nonlinear oscillators, modeled by sine circle maps, with varying degrees of randomness in coupling connections. We show that the change in the basin of attraction of the spatiotemporal fixed point due to varying fraction of random links $p$, is crucially related to the nature of the local dynamics. Even the qualitative dependence of spatiotemporal regularity on $p$ changes drastically as the angular frequency of the oscillators change, ranging from monotonic increase or monotonic decrease, to non-monotonic variation. Thus it is evident here that the influence of random coupling connections on spatiotemporal order is highly non-universal, and depends very strongly on the nodal dynamics.