Self-organized network evolution coupled to extremal dynamics

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak‐ Sneppen evolution model with the rules of the so-calledfitness network model for establishing the topology of a network; each vertex is assigned a ‘fitness’, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that di ers from what is obtained when the two processesaredecoupled.Apower-lawdecayofdynamicalandtopologicalquantitiesaboveathresholdemergesspontaneously,aswell as a feedback between di erent dynamical regimes and the underlying correlation and percolation properties of the network.

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