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We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention in the interplay between networks topological disorder and its synchronization features. Firstly, we analyze synchronization time $T$ in random networks, and find a scaling law which relates $T$ to networks connectivity. Then, we carry on comparing synchronization time for several other topological configurations, characterized by a different degree of randomness. The analysis shows that regular lattices perform better than any other disordered network. The fact can be understood by considering the variability in the number of links between two adjacent neighbors. This phenomenon is equivalent to have a non-random topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings.
We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling dela
The effects of nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange of electrical signals between neurons. Earlier investigations have demonstrated that non-local and
The human cortex is never at rest but in a state of sparse and noisy neural activity that can be detected at broadly diverse resolution scales. It has been conjectured that such a state is best described as a critical dynamical process -- whose natur
A lattice of three-state stochastic phase-coupled oscillators introduced by Wood it et al. exhibits a phase transition at a critical value of the coupling parameter $a$, leading to stable global oscillations (GO). On a complete graph, upon further in
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability approach, w