Concurrent enhancement of percolation and synchronization in adaptive networks.

Young-Ho Eom,Guido Caldarelli,Stefano Boccaletti

doi:10.1038/srep27111

Abstract

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems’ collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems.

Highlights

Component), achieving global functions may be hampered by the absence of stable interactions between the units
We assign initial conditions for the oscillators’ phases from a uniformly distributed distribution in the range [−π, π], while the initial network structure is taken to be that extracted from Eq (2) with the given initial phases
When t < 0, the time evolution of the order parameters is determined by the fixed network structure constructed by Eq 2 with the initial phases, whereas the network structure is updated by Eq 2 at every time step

Summary

The Adaptive Network Model

We start by considering a network of N (Kuramoto-type) phase oscillators[35,36], whose time evolution is ruled by: dθi dt. The structure of connections is given by the so-called fitness or hidden variable network model[37,38], which is a generalized Erdös-Reyni (ER) model. The distinctive character of such a model is that the topology is fully shaped by the fitness of the nodes ( associated to the oscillators’ phases) while the topology is given by a constant probability in the ER model. The connection probability between two node i and j at time t is determined by a given function f(θi, θj). While the form of function f can be, in general, arbitrary, we here consider it to follow a homophily principle, through which oscillators with more similar phases are more likely to be connected.

Results

Discussion

Additional Information