Role of time scales and topology on the dynamics of complex networks

TL;DR

This paper investigates how different time scales and network topology influence the collective dynamics of complex networks of nonlinear oscillators, revealing phenomena like amplitude death, synchronization transitions, and the effects of heterogeneity.

Contribution

It introduces a comprehensive analysis of the impact of slow systems and network heterogeneity on dynamical behaviors and critical transitions in complex oscillator networks.

Findings

Transition to amplitude death with increased slow systems

Scaling laws near synchronization transitions

Heterogeneity leads to self-organized frequency states

Abstract

The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the emergence of such phenomena and their transitions by considering a complex network of dynamical systems in which a fraction of systems evolves on a slower time scale on the network. We report the transition to amplitude death for the whole network and the scaling near the transitions as the connectivity pattern changes. We also discuss the suppression and recovery of oscillations and the cross over behavior as the number of slow systems increases. By considering a scale free network of systems with multiple time scales, we study the role of heterogeneity in link structure on dynamical properties and the consequent critical behaviors. In this case with hubs made slow, our main results are the escape time statistics for loss of complete synchrony as the slowness spreads on the network and the self-organization of the whole network to a new frequency synchronized state. Our results have potential applications in biological, physical, and engineering networks consisting of heterogeneous oscillators.