Related papers: Nonequilibrium Phase Transitions in Directed Small…
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…
Societies experience politically stable and unstable phases along history, whereas political power is usually passed to new elite groups by these changes. Structural dynamics of the elites in a society have been proposed to be one of the…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
In this paper, we investigate the self-affirmation effect on formation of public opinion in a directed small-world social network. The system presents a non-equilibrium phase transition from a consensus state to a disordered state with…
Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a…
Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
Mostly acyclic directed networks, treated mathematically as directed graphs, arise in machine learning, biology, social science, physics, and other applications. Newman [1] has noted the mathematical challenges of such networks. In this…
Binary mixtures growing on small-world networks under far-from-equilibrium conditions are studied by means of extensive Monte Carlo simulations. For any positive value of the shortcut fraction of the network ($p>0$), the system undergoes a…
The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
In many real-world networks the ability to synchronize is a key property for its performance. Examples include power-grid, sensor, and neuron networks as well as consensus formation. Recent work on undirected networks with diffusive…
We present, as a very general method, an effective field theory to analyze models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it gives the exact…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real…