Related papers: Scale-free patterns at a saddle-node bifurcation i…
This paper develops a framework for analyzing and designing dynamic networks comprising different classes of nodes that coexist and interact in one shared environment. We consider {\em ad hoc} (i.e., nodes can leave the network unannounced,…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We extend the stationary-state work fluctuation theorem to periodically modulated nonlinear systems. Such systems often have coexisting stable periodic states. We show that work fluctuations sharply increase near a kinetic phase transition…
A simple model of activatory-inhibitory interactions controlling the activity of agents (substrates) through a "saturated response" dynamical rule in a scale-free network is thoroughly studied. After discussing the most remarkable dynamical…
We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) random scale-free topology, (ii)…
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
In this paper we present a deterministic vertex spawning model that yields a scale-free network. The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree…
We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for biological evolution in scale-free networks. By using large scale numerical simulations, we study the avalanche size distribution and the activity…
Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This…
We study the relaxation of the bi-dimensional kinetically constrained spiral model. We show that due to the reversibility of the dynamic rules any unblocked state fully decorrelates in finite times irrespectively of the system being in the…
Animal motion and flocking are ubiquitous nonequilibrium phenomena that are often studied within active matter. In examples such as insect swarms, macroscopic quantities exhibit power laws with measurable critical exponents and ideas from…
Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…
The body plan of the fruit fly is determined by the expression of just a handful of genes. We show that the spatial patterns of expression for several of these genes scale precisely with the size of the embryo. Concretely, discrete…
In this work we study a simple evolutionary model of bipartite networks which its evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary…
Originally, protocols were designed for multi-agent systems (MAS) using information about the network which might not be available. Recently, there has been a focus on scale-free synchronization where the protocol is designed without any…
We give conditions under which a scalar random variable T can be coupled to a random scaling factor $\xi$ such that T and $\xi$T are rendered stochastically independent. A similar result is obtained for random measures. One consequence is a…