Universality in network dynamics

Universality in network dynamics

Despite significant advances in characterizing the structural properties of complex networks, a mathematical framework that uncovers the universal properties of the interplay between the topology and the dynamics of complex systems continues to elude us. Here we develop a self-consistent theory of dynamical perturbations in complex systems, allowing us to systematically separate the contributio...

Universality in network dynamics Supplementary Information

Hot spots and universality in network dynamics

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding evidence of orders of magnitude differences in the fluxes of individual nodes. This dynamical inhomogeneity reflects the emerg...

Universality of cluster dynamics.

We have studied the kinetics of cluster formation for dynamical systems of dimensions up to n=8 interacting through elastic collisions or coalescence. These systems could serve as possible models for gas kinetics, polymerization, and self-assembly. In the case of elastic collisions, we found that the cluster size probability distribution undergoes a phase transition at a critical time which can...

Universality of causal graph dynamics

Causal Graph Dynamics generalize Cellular Automata, extending them to bounded degree, time varying graphs. The dynamics rewrite the graph at each time step with respect to two physics-like symmetries: causality (bounded speed of information) and homogeneity (the rewriting acts the same everywhere on the graph, at every time step). Universality is the ability simulating every other instances of ...