Publications -- syncronization

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  Control of coupled oscillator networks with application to microgrid technologies

Science Advances 1, 7 - DOI: 10.1126/sciadv.1500339 - 2015

P.S. Skardal and A. Arenas

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions—a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.

  Emergence of assortative mixing between clusters of cultured neurons

PLOS Comput. Biol. 10(9), e1003796 - - 2014

S. Teller, C. Granell, M. De Domenico, J. Soriano, S. Gomez, A. Arenas

The analysis of the activity of neuronal cultures is considered to be a good proxy of the functional connectivity of in vivo neuronal tissues. Thus, the functional complex network inferred from activity patterns is a promising way to unravel the interplay between structure and functionality of neuronal systems. Here, we monitor the spontaneous self-sustained dynamics in neuronal cultures formed by interconnected aggregates of neurons (clusters). Dynamics is characterized by the fast activation of groups of clusters in sequences termed bursts. The analysis of the time delays between clusters' activations within the bursts allows the reconstruction of the directed functional connectivity of the network. We propose a method to statistically infer this connectivity and analyze the resulting properties of the associated complex networks. Surprisingly enough, in contrast to what has been reported for many biological networks, the clustered neuronal cultures present assortative mixing connectivity values, meaning that there is a preference for clusters to link to other clusters that share similar functional connectivity, as well as a rich-club core, which shapes a ‘connectivity backbone’ in the network. These results point out that the grouping of neurons and the assortative connectivity between clusters are intrinsic survival mechanisms of the culture.

  Disorder induces explosive synchronization

Physical Review E 89, 062811 - DOI: - 2014

P. S. Skardal and A. Arenas

We study explosive synchronization, a phenomenon characterized by first-order phase transitions between incoherent and synchronized states in networks of coupled oscillators. While explosive synchronization has been the subject of many recent studies, in each case strong conditions on either the heterogeneity of the network, its link weights, or its initial construction are imposed to engineer a first-order phase transition. This raises the question of how robust explosive synchronization is in view of more realistic structural and dynamical properties. Here we show that explosive synchronization can be induced in mildly heterogeneous networks by the addition of quenched disorder to the oscillators’ frequencies, demonstrating that it is not only robust to, but moreover promoted by, this natural mechanism. We support these findings with numerical and analytical results, presenting simulations of a real neural network as well as a self-consistency theory used to study synthetic networks.

  Modeling self-sustained activity cascades in socio-technical networks

Europhysics Letters, 104, 48004 - - 2013

P. Piedrahita, J. Borge-Holthoefer, Y. Moreno and A. Arenas

The ability to understand and eventually predict the emergence of information and activation cascades in social networks is core to complex socio-technical systems research. However, the complexity of social interactions makes this a challenging enterprise. Previous works on cascade models assume that the emergence of this collective phenomenon is related to the activity observed in the local neighborhood of individuals, but do not consider what determines the willingness to spread information in a time-varying process. Here we present a mechanistic model that accounts for the temporal evolution of the individual state in a simplified setup. We model the activity of the individuals as a complex network of interacting integrate-and-fire oscillators. The model reproduces the statistical characteristics of the cascades in real systems, and provides a framework to study the time evolution of cascades in a state-dependent activity scenario.