This letter focus on the effect of repulsive interactions on the adoption of an external message in an opinion model. With a simple change in the rules, we modify the Deffuant et al. model to incorporate the presence of repulsive interactions. We will show that information receptiveness is optimal for an intermediate fraction of repulsive links. Using the master equation as well as Monte Carlo simulations of the message-free model, we identify the point where the system becomes optimally permeable to external influence with an order-disorder transition.

We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external signal is optimal for a particular proportion of repulsive links. Furthermore, we show that a resonance also occurs for other system parameters, like the coupling strength and the number of elements. We relate this resonance to the appearance of a multistable region, and we predict the location of the resonance peaks, by a simple spectral analysis of the Laplacian matrix.

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.

We revisit a recently introduced agent model [ACS 11, 99 (2008)], where economic growth is a consequence of education (human capital formation) and innovation, and investigate the influence of the agents' social network, both on an agent's decision to pursue education and on the output of new ideas. Regular and random networks are considered. The results are compared with the predictions of a mean field (representative agent) model.

We consider a system of identical van der Pol oscillators, globally coupled through their velocities, and study how the presence of competitive interactions affects its synchronisation properties. We will address the question from two points of view. Firstly, we will investigate the role of competitive interactions on the synchronisation among identical oscillators. Then, we will show that the presence of an intermediate fraction of repulsive links results in the appearance of macroscopic oscillations at that signal's rhythm, in regions where the individual oscillator is unable to synchronise with a weak external signal. §1. Introduction Synchronisation, 1) or the ability of coupled oscillators to adjust their rhythms, is a property that arises in many systems, from pacemaker cells in the heart firing simultaneously as a result of their interaction, 2) to the fetal heart rate adjusting its pace to maternal breathing, as an example of forced synchronisation. 3) Typically, oscillators with different frequencies are able to synchronise due to a strong enough positive coupling among units. However, interactions in Nature are often repulsive and, surprisingly, it was found that under some particular circumstances repulsive interactions can actually enhance synchronisation: thus, the presence of negative links can prevent the instability of the fully synchronised state when it compensates an excessive number of positive links, 4) or its sparse presence can enhance synchronisation in small-world networks. 5) Most interestingly -since it is not always desirable to achieve a state of full synchronisation -the presence of repulsive links can give rise to new forms of synchronisation, 6) that sometimes can be described as glassy or glassy-like. 8), 9), 10), 7) Additionally, the beam-forming abilities of a system of repulsively coupled Stuart-Landau oscillators were considered in. 11)So far, studies have mostly focused on non-identical phase oscillators, and several coupling schemes have been chosen, such as local 12) or long-range, 5) and purely repulsive 6) or assuming a competition between repulsive and attractive. 13) Like in, 13) we want to isolate the effect of different proportions of repulsive interactions by considering identical oscillators. However, rather than establishing how full synchronisation becomes unstable as the fraction p of repulsive links increases, 13) our focus will be on the characterisation of the different configurations that emerge as p grows, and its implications for signal transmission when the system is subjected to an external forcing. Also, unlike 13) we will not consider phase oscillators, but instead van der Pol oscillators, 14) which implies phase, amplitude and frequency synchronisation are taken into consideration. typeset using PTPT E X.cls Ver.0.9

In nonlinear systems, the right amount of noise can amplify the response to a weak periodic signal, by a phenomenon known as stochastic resonance 1. It was shown that the same constructive role can be played by any source of disorder 2 We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links. The system is subjected to a sub-threshold periodic 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 spinlike neurons with excitatory and inhibitory couplings. By means of numerical simulations, we find that there is an optimal probability of repulsive links, such that the coherent response is maximal, and we propose a mechanism to explain this resonance.