Divide and conquer: resonance induced by competitive interactions

We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links and subjected to a periodic subthreshold signal. By means of numerical simulations and analytical calculations we give evidence that the global response of the system reaches a maximum value for a given fraction of the number of repulsive interactions. The model can represent a network of spin-like neurons with excitatory and inhibitory couplings, or a simple opinion spreading model. In this context, attractive/repulsive links represent friends and enemies. “Divide and Conquer” refers to the fact that in order to force a society to adopt a new point of view, it helps to break its homogeneity by fostering enmities amongst its members.