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It was observed that the spatiotemporal chaos in lattices of coupled chaoticmaps was suppressed to a spatiotemporal fixed point when some fraction of theregular coupling connections were replaced by random links. Here we investigatethe effects of different kinds of parametric fluctuations on the robustness ofthis spatiotemporal fixed point regime. In particular we study thespatiotemporal dynamics of the network with noisy interaction parameters,namely fluctuating fraction of random links and fluctuating coupling strengths.We consider three types of fluctuations: (i) noisy in time, but homogeneous inspace; (ii) noisy in space, but fixed in time; (iii) noisy in both space andtime. We find that the effect of different kinds of parameteric noise on thedy- namics is quite distinct: quenched spatial fluctuations are the mostdetrimental to spatiotemporal regularity; spatiotemporal fluctuations yieldphenomena similar to that observed when parameters are held constant at themean-value; and interestingly, spatiotemporal regularity is most robust underspatially uniform temporal fluctuations, which in fact yields a larger fixedpoint range than that obtained under constant mean-value parameters.

Under what kind of parametric fluctuations is spatiotemporal regularity the most robust?