A note on the consensus time of mean-field majority-rule dynamics

In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes. This is determined by the size distribution of the groups that, at each evolution step, gather to reach agreement. When the group size distribution has a finite mean value, the previously known logarithmic dependence on the population size holds. On the other hand, when the mean group size diverges, the consensus time and the population size are related through a power law. Numerical simulations validate this semi-quantitative analytical prediction.Comment: 4 pages, 3 figures, Commentary and Reply available in Papers in Physic

SIR epidemics in monogamous populations with recombination

We study the propagation of an SIR (susceptible-infectious-recovered) disease over an agent population which, at any instant, is fully divided into couples of agents. Couples are occasionally allowed to exchange their members. This process of couple recombination can compensate the instantaneous disconnection of the interaction pattern and thus allow for the propagation of the infection. We study the incidence of the disease as a function of its infectivity and of the recombination rate of couples, thus characterizing the interplay between the epidemic dynamics and the evolution of the population's interaction pattern.Comment: 7 pages, 3 figure

Synchronization and structure in an adaptive oscillator network

We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.Comment: 6 pages, 7 figure

Synchronised firing induced by network dynamics in excitable systems

We study the collective dynamics of an ensemble of coupled identical FitzHugh--Nagumo elements in their excitable regime. We show that collective firing, where all the elements perform their individual firing cycle synchronously, can be induced by random changes in the interaction pattern. Specifically, on a sparse evolving network where, at any time, each element is connected with at most one partner, collective firing occurs for intermediate values of the rewiring frequency. Thus, network dynamics can replace noise and connectivity in inducing this kind of self-organised behaviour in highly disconnected systems which, otherwise, wouldn't allow for the spreading of coherent evolution.Comment: 5 pages, 5 figure

Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators

We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled -contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators -and, in particular, micromechanical oscillators- provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phase-shift control oscillations are stable over the whole resonance curve. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices

Avoiding extinction by migration: The case of the head louse

The possibility of spreading by migration, colonizing new spatial domains suitable for development and reproduction, can substantially relieve a biological population from the risk of extinction. By means of a realistic computational model based on empirical data, we study this phenomenon for the human head louse, Pediculus humanus capitis. In particular, we show that a lice colony infesting a single isolated host is prone to extinction by stochastic population fluctuations within an interval of several months, while migration over a relatively small group of hosts in contact with each other is enough to insure the prevalence of the infestation for indefinitely long periods. We characterize the interplay of the size of the host group with the host-to-host contagion probability, which controls a transition between extinction of the lice population and a situation where the infestation is endemic

Critical phenomena in the spreading of opinion consensus and disagreement

We consider a class of models of opinion formation where the dissemination of individual opinions occurs through the spreading of local consensus and disagreement. We study the emergence of full collective consensus or maximal disagreement in one- and two-dimensional arrays. In both cases, the probability of reaching full consensus exhibits well-defined scaling properties as a function of the system size. Two-dimensional systems, in particular, possess nontrivial exponents and critical points. The dynamical rules of our models, which emphasize the interaction between small groups of agents, should be considered as complementary to the imitation mechanisms of traditional opinion dynamics.Comment: 9 pages, 10 figure