Optimized network structure for full-synchronization. (English) Zbl 1221.34143
Summary: A network of Kuramoto oscillators with different natural frequencies is optimized for enhanced synchronizability. All node inputs are normalized by the node connectivity and some important properties of the network structure are determined in this case: (i) optimized networks present a strong anti-correlation between natural frequencies of adjacent nodes; (ii) this anti-correlation should be as high as possible since the average path length between nodes is maintained as small as in random networks; and (iii) high anti-correlation is obtained without any relation between nodes natural frequencies and the degree of connectivity. We also propose a network construction model with which it is shown that high anti-correlation and small average paths may be achieved by randomly rewiring a fraction of the links of a totally anti-correlated network, and that these networks present optimal synchronization properties.
MSC:
| 34D20 | Stability of solutions to ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34C29 | Averaging method for ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
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