Divide and conquer: resonance induced by competitive interactions

Abstract

We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links. This system is subjected to a subthreshold signal, and the goal is to see how the response is enhanced for a given fraction of repulsive links. This can model a network of spin-like neurons with excitatory and inhibitory couplings. By means of numerical simulations and analytical calculations we find that there is an optimal probability, such that the coherent response is maximal.

Mass media and repulsive interactions in continuous-opinion dynamics

“…When the signal frequency decreases, this optimal region shrinks until it coincides with the order-disorder transition point. The same coincidence was noticed in previous studies [11,13,14] showing an optimal response induced by diversity or competitive interactions, and we conclude that it is expected in extended systems where some of the units can be in a state that is inaccessible to the external signal, whether it is because of the existence of a potential barrier like in the previous works, or because of a threshold of interaction. We saw that the presence of repulsive links and consequent dispersion of opinions is a necessary condition for a collective adoption of the message, by increasing the number of agents within t he reach of propaganda.…”

“…This counterintuitive result is reminiscent of studies in which the presence of some kind of disorder -like noise [8][9][10], diversity [11,12] or competitive interactions [13,14] -enhances the response to a weak time-dependant signal. Typically in those systems, the individual units have some stable states that can only be left or accessed by overcoming a barrier that a weak signal alone is not enough to surpass.…”

Diversity-Induced Resonance in a System of Globally Coupled Linear Oscillators

“…This explanation sheds new light on the phenomenon of stochastic resonance in extended systems [8,9] in which the disorder is induced by noise. In other cases, it is the disorder induced by the competitions in the network of connectivities between the units that induces disorder and drives the resonance [10]. As argued in reference [6] the proposed mechanism is generic and might appear in a large variety of systems of interest in many different fields.…”

Non Local Effects in the Sznajd Model: Stochastic resonance aspects

“…We have studied the phenomenon of stochastic resonance (SR) [11], which consists in an enhancement of the system's response when subjected to the action of a periodical external field (the fashion or propaganda) when the internal noise (in this case, the social temperature) reaches an optimal value. Within this social context, SR was previously studied by several authors [13,[15][16][17][18]. As a complement to a previous work [20], we also analyze the effect of introducing some degree of non locality in the selection of those agents whose opinion is modified at each time step.…”