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

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