Spontaneous repulsion in the [Formula: see text] reaction on coupled networks

We study the transient dynamics of an [Formula: see text] process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions [Formula: see text] of cross couplings, the concentration of [Formula: see text] (or [Formula: see text]) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time [Formula: see text]. By numerical and analytical arguments, we show that for symmetric and homogeneous structures [Formula: see text] where [Formula: see text] is the mean degree of both networks. Being this behavior is in marked contrast with a purely diffusive process, where the mixing time would go simply like [Formula: see text] , we identify the logarithmic slowing down in [Formula: see text] to be the result of a spontaneous mechanism of repulsion between the reactants [Formula: see text] and [Formula: see text] due to the interactions taking place at the networks' interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.