Optimized inter-structure for enhancing the synchronizability of interdependent networks

In this paper, how to optimize the inter-structures to enhance the synchronizability of interdependent networks is investigated. Based on a genetic algorithm (GA), combined with two fitness functions, a new method is presented that optimizes inter-structures to enhance the synchronizability of interdependent networks. For bounded and unbounded synchronous regions, when the number of inter-connections or the inter-coupling strength related to the inter-structures is changed, we apply the proposed method to optimize the two interdependent networks. The first network, namely NW–BA network, includes a small-world subnet generated by Newman–Watts algorithm and a Barabá si–Albert scale-free subnet. The second network, ST–BA network, includes a star subnet and a BA subnet. Generally, the analyses and numerical simulation results demonstrate the proposed optimization method performs well. According to the betweenness correlation defined in this paper, as the number of inter-connections increase, the optimized inter-structures experience a process that shifts a nearly positive correlation to irrelevance. However, increasing the inter-coupling strength gradually makes no difference on optimized inter-structures. Overall, the results indicate that NW–BA networks are a better choice for interdependent networks than the ST–BA networks.