空间嵌入振荡网络生长的贪婪优化
Greedy optimization for growing spatially embedded oscillatory networks
摘要：
某些类型的振荡器的耦合需要它们之间的物理链路的调解，使得振荡器之间的距离成为实现同步的关键因素。在本文中，我们提出并探讨了一个贪婪算法来增长空间嵌入振荡器网络。该算法的构造方式是按顺序增加节点，以最小化增加的链路长度的代价和优化增长网络的线性稳定性。我们表明，对于适当的参数，所得到的网络的稳定性，测量的动态小扰动和相关长度的干扰，可以显着提高以最小的增加长度成本。此外，我们数值分析所得到的网络的拓扑性质，并发现，虽然更稳定，其度分布近似指数和算法参数无关。此外，我们发现其他与网络弹性和效率相关的拓扑参数也受到该算法的影响。最后，我们将我们的研究结果扩展到具有不同异质性来源的更一般的网络类别。我们的研究结果是第一步，在发展算法的振荡网络具有理想的稳定性，动力学和拓扑性质的定向增长。
英文摘要：
The coupling of some types of oscillators requires the mediation of a physical link between them, rendering the distance between oscillators a critical factor to achieve synchronization. In this paper we propose and explore a greedy algorithm to grow spatially embedded oscillator networks. The algorithm is constructed in such a way that nodes are sequentially added seeking to minimize the cost of the added links' length and optimize the linear stability of the growing network. We show that, for appropriate parameters, the stability of the resulting network, measured in terms of the dynamics of small perturbations and the correlation length of the disturbances, can be significantly improved with a minimal added length cost. In addition, we analyze numerically the topological properties of the resulting networks and find that, while being more stable, their degree distribution is approximately exponential and independent of the algorithm parameters. Moreover, we find that other topological parameters related with network resilience and efficiency are also affected by the proposed algorithm. Finally, we extend our findings to more general classes of networks with different sources of heterogeneity. Our results are a first step in the development of algorithms for the directed growth of oscillatory networks with desirable stability, dynamical and topological properties.
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