Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations

We study the effect of spatial frequency-forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of polarized light waves. We show that forcing introduces spatial modulations on standing waves which remain frequency locked with a forcing-independent frequency. For forcing above a threshold the modulated standing waves unlock, bifurcating into a temporally periodic state. Below the threshold the system presents a kind of excitability.Comment: 4 pages, including 4 postscript figures. To appear in Physical Review Letters (1996). This paper and related material can be found at http://formentor.uib.es/Nonlinear

Synchronization of Spatiotemporal Chaos: The regime of coupled Spatiotemporal Intermittency

Synchronization of spatiotemporally chaotic extended systems is considered in the context of coupled one-dimensional Complex Ginzburg-Landau equations (CGLE). A regime of coupled spatiotemporal intermittency (STI) is identified and described in terms of the space-time synchronized chaotic motion of localized structures. A quantitative measure of synchronization as a function of coupling parameter is given through distribution functions and information measures. The coupled STI regime is shown to dissapear into regular dynamics for situations of strong coupling, hence a description in terms of a single CGLE is not appropiate.Comment: 4 pages, LaTeX 2e. Includes 3 figures made up of 8, 4 (LARGE),and 2 postscript files. Includes balanced.st

Phase Synchronization and Polarization Ordering of Globally-Coupled Oscillators

We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions: to phase synchronization and to polarization ordering. Introducing a global-phase and a polarization order parameters, we show that the transition to global-phase synchrony is found when the coupling overcomes a critical value and that polarization order enhancement can not take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results

Enhancing the superconducting transition temperature of BaSi2 by structural tuning

We present a joint experimental and theoretical study of the superconducting phase of the layered binary silicide BaSi2. Compared with the layered AlB2 structure of graphite or diboride-like superconductors, in the hexagonal structure of binary silicides the sp3 arrangement of silicon atoms leads to corrugated sheets. Through a high-pressure synthesis procedure we are able to modify the buckling of these sheets, obtaining the enhancement of the superconducting transition temperature from 4 K to 8.7 K when the silicon planes flatten out. By performing ab-initio calculations based on density functional theory we explain how the electronic and phononic properties of the system are strongly affected by changes in the buckling. This mechanism is likely present in other intercalated layered superconductors, opening the way to the tuning of superconductivity through the control of internal structural parameters.Comment: Submitte

Network coevolution drives segregation and enhances Pareto optimal equilibrium selection in coordination games

In this work we assess the role played by the dynamical adaptation of the interactions network, among agents playing Coordination Games, in reaching global coordination and in the equilibrium selection. Specifically, we analyze a coevolution model that couples the changes in agents’ actions with the network dynamics, so that while agents play the game, they are able to sever some of their current connections and connect with others. We focus on two action update rules: Replicator Dynamics (RD) and Unconditional Imitation (UI), and we define a coevolution rule in which, apart from action updates, with a certain rewiring probability p, agents unsatisfied with their current connections are able to eliminate a link and connect with a randomly chosen neighbor. We call this probability to rewire links the ‘network plasticity’. We investigate a Pure Coordination Game (PCG), in which choices are equivalent, and on a General Coordination Game (GCG), for which there is a risk-dominant action and a payoff-dominant one. Changing the plasticity parameter, there is a transition from a regime in which the system fully coordinates on a single connected component to a regime in which the system fragments in two connected components, each one coordinated on a different action (either if both actions are equivalent or not). The nature of this fragmentation transition is different for different update rules. Second, we find that both for RD and UI in a GCG, there is a regime of intermediate values of plasticity, before the fragmentation transition, for which the system is able to fully coordinate on a single component network on the payoff-dominant action, i.e., coevolution enhances payoff-dominant equilibrium selection for both update rules

Importance of single nodes in dynamics on networks

Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single out the role of individual elements in such intermingled systems, or which is the best way to quantify their importance. Centrality measures describe a node's importance by its position in a network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely determined by the structure of the system but it is a result of the interplay between dynamics and network structure

Analytical and numerical study of the non-linear noisy voter model on complex networks

We study the noisy voter model using a specific non-linear dependence of the rates that takes into account collective interaction between individuals. The resulting model is solved exactly under the all-to-all coupling configuration and approximately in some random networks environments. In the all-to-all setup we find that the non-linear interactions induce "bona fide" phase transitions that, contrary to the linear version of the model, survive in the thermodynamic limit. The main effect of the complex network is to shift the transition lines and modify the finite-size dependence, a modification that can be captured with the introduction of an effective system size that decreases with the degree heterogeneity of the network. While a non-trivial finite-size dependence of the moments of the probability distribution is derived from our treatment, mean-field exponents are nevertheless obtained in the thermodynamic limit. These theoretical predictions are well confirmed by numerical simulations of the stochastic process

Stochastic pair approximation treatment of the noisy voter model

We present a full stochastic description of the pair approximation scheme to study binary-state dynamics on heterogeneous networks. Within this general approach, we obtain a set of equations for the dynamical correlations, fluctuations and finite-size effects, as well as for the temporal evolution of all relevant variables. We test this scheme for a prototypical model of opinion dynamics known as the noisy voter model that has a finite-size critical point. Using a closure approach based on a system size expansion around a stochastic dynamical attractor we obtain very accurate results, as compared with numerical simulations, for stationary and time dependent quantities whether below, within or above the critical region. We also show that finite-size effects in complex networks cannot be captured, as often suggested, by merely replacing the actual system size $N$ by an effective network dependent size $N_{{\rm eff}}