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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 8: Poster

SOE 8.23: Poster

Montag, 16. März 2015, 18:00–20:00, Poster E

Heterogeneity in synchronizing networks of mobile particles — •Jorge P. Rodríguez and Víctor M. Eguíluz — Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain

The Kuramoto model of synchronization proposes an interaction between particles which, in the case of every particle having the same natural frequency, makes their phases approach. We will explore the Fujiwara model, which considers that the particles move diffusively in a square, and they only interact via a Kuramoto update with the particles that are located within their circular zone of influence. Hence, we have a temporal random geometric graph, as the motion of particles modifies the topology of the spatial network.

First of all, we analyse the synchronization process if there is a fraction p of slow particles (1−p of fast). Comparing this process with that of a set of particles moving with the same homogeneous average velocity, we find that the heterogeneous case is slightly slower than the homogeneous. In order to characterize the role of heterogeneity, we consider a system with a Gaussian distribution of particle velocities, and analyze the characteristic synchronization time as a function of the distribution width. We find that the heterogeneity modifies the average relative velocity between particles, which is related with the average link time duration, influencing the characteristic synchronization time.

Finally, we consider that faster particles have a bigger zone of interaction. Links will be directed, and we will find a threshold for the width above which there is no global synchronization.