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The transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small-world networks. The local dynamics is given by the Chate-Manneville minimal map previously used in studies of spatiotemporal intermittency in ordered lattices. The critical boundary separating laminar and turbulent regimes is calculated on the parameter space of the system, given by the coupling strength and the rewiring probability of the network. Windows of relaminarization are present in some regions of the parameter space. New features arise in small-world networks; for instance, the character of the transition to turbulence changes from second order to a first order phase transition at some critical value of the rewiring probability. A linear relation characterizing the change in the order of the phase transition is found. The global quantity used as order parameter for the transition also exhibits nontrivial collective behavior for some values of the parameters. These models may describe several processes occurring in nonuniform media where the degree of disorder can be continuously varied through a parameter.
Small-world networks describe many important practical systems among which neural networks consisting of excitable nodes are the most typical ones. In this paper we study self-sustained oscillations of target waves in excitable small-world networks.
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point re
Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical sequence of
The small-world transition is a first-order transition at zero density $p$ of shortcuts, whereby the normalized shortest-path distance undergoes a discontinuity in the thermodynamic limit. On finite systems the apparent transition is shifted by $Delt
We investigate supervised learning in neural networks. We consider a multi-layered feed-forward network with back propagation. We find that the network of small-world connectivity reduces the learning error and learning time when compared to the netw