Spontaneous formation of dynamical groups in an adaptive networked system

Menghui Li,Shuguang Guan,C-H Lai

doi:10.1088/1367-2630/12/10/103032

Abstract

In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously differentiate into two dynamical groups after a long time evolution. Within each group, the oscillators have similar phases, while oscillators in different groups have approximately opposite phases. The network gradually converts from the initial random structure with a uniform distribution of connection strengths into a modular structure that is characterized by strong intra-connections and weak inter-connections. Furthermore, the connection strengths follow a power-law distribution, which is a natural consequence of the coevolution of the network and the dynamics. Interestingly, it is found that if the inter-connections are weaker than a certain threshold, the two dynamical groups will almost decouple and evolve independently. These results are helpful in further understanding the empirical observations in many social and biological networks.

Highlights

Modularity frequently occurs in many social and biological networked systems [1], which is generally believed to correspond to certain functional groups [2]
The change of the synaptic coupling strength between neurons depends on the relative timing of the presynaptic and postsynaptic spikes in neural networks [19], and in the mobile communication networks [3], the connection strengths are determined by the dynamical behaviors of the mobile agents
We noticed that in many social and biological networked systems, with the evolution of the network topology, dynamically the system may form different functional groups corresponding to different dynamical states

Summary

Introduction

Modularity frequently occurs in many social and biological networked systems [1], which is generally believed to correspond to certain functional groups [2]. In adaptive oscillator networks where the connections are coupled with the dynamical states, the order parameters R and F can be jointly used to characterize whether the local coherence within subnetwork takes place. After a long time evolution from random initial phases on random networks, it indicates that the local synchronization (rather than the global synchronization) emerges within subnetworks, i.e., the dynamical groups have been generated in the system.

Results

Conclusion