Rapidly switched random links enhance spatiotemporal regularity

We investigate the spatiotemporal properties of a lattice of chaotic maps whose coupling connections are rewired to random sites with probability p. Keeping p constant, we change the random links at different frequencies in order to discern the effect (if any) of the time dependence of the links. We observe two different regimes in this network: (i) when the network is rewired slowly, namely, when the random connections are quite static, the dynamics of the network is spatiotemporally chaotic and (ii) when these random links are switched around fast, namely, the network is rewired frequently, one obtains a spatiotemporal fixed point over a large range of coupling strengths. We provide evidence of a sharp transition from a globally attracting spatiotemporal fixed point to spatiotemporal chaos as the rewiring frequency is decreased. Thus, in addition to geometrical properties such as the fraction of random links in the network, dynamical information on the time dependence of these links is crucial in determining the spatiotemporal properties of complex dynamical networks.