Design of functional network dynamics and universality

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We design the network of oscillators to improve synchronization properties through appropriate rewiring of its connections. We consider what are the optimal network architectures for a given total number of connections. Starting with an initial random network of oscillators, its autonomous synchronization ability can be largely improved by appropriately rewiring the links between the elements using the Markov chain Monte Carlo method. The architectures of such optimal networks strongly depend on the constraints, such as the total number of links available. Through the appropriate rewiring of a network, a strong gain in the synchronization signal can be achieved. It is also shown that the architectures leading to the improved synchronization of identical oscillators in the presence of noise are essentially different from the optimal synchronization architectures for heterogeneous oscillator populations without noise. Large ensembles of optimized networks are obtained and their statistical properties have been investigated. These results are published in Phys. Rev. E.