Does dynamics reflect topology in directed networks?

Abstract

We present and analyze a topologically induced transition from ordered, synchronized to disordered dynamics in directed networks of oscillators. The analysis reveals where in the space of networks this transition occurs and its underlying mechanisms. If disordered, the dynamics of the units is precisely determined by the topology of the network and thus characteristic for it. We develop a method to predict the disordered dynamics from topology. The results suggest a new route towards understanding how the precise dynamics of the units of a directed network may encode information about its topology.

7 pages, 4 figures, Europhysics Letters, accepted

References in corpus (11)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Evolution of networks
• Synchronization reveals topological scales in complex networks
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators
• Entrainment of randomly coupled oscillator networks by a pacemaker
• Breaking Synchrony by Heterogeneity in Complex Networks
• Long Chaotic Transients in Complex Networks
• Propagation of small perturbations in synchronized oscillator networks
• Long range action in networks of chaotic elements

Cited by in corpus (24)

• Critical phenomena in complex networks
• Revealing Network Connectivity From Dynamics
• Inferring Network Topology from Complex Dynamics
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Revealing networks from dynamics: an introduction
• The Emergence of El-Niño as an Autonomous Component in the Climate Network
• Synchronizability determined by coupling strengths and topology on Complex Networks
• Transient Uncoupling Induces Synchronization
• Reconstructing Links in Directed Networks from Noisy Dynamics
• A universal order parameter for synchrony in networks of limit cycle oscillators
• Do Small Worlds Synchronize Fastest?
• Rhythmogenic neuronal networks, pacemakers, and k-cores
• Does the brain behave like a (complex) network? I. Dynamics
• Speed of complex network synchronization
• Synchronizing noisy nonidentical oscillators by transient uncoupling
• Synchrony for weak coupling in the complexified Kuramoto model
• Effects of hidden nodes on the reconstruction of bidirectional networks
• Optimal synchronization on strongly connected directed networks
• Connectivity and Dynamics of Neuronal Networks as Defined by the Shape of Individual Neurons
• Complexified Synchrony
• Spatiotemporal phase synchronization in a large array of convective oscillators
• Synchronization on directed small worlds: feed forward loops and cycles
• Transition from the self-organized to the driven dynamical clusters