How to grow an oscillator network with enhanced synchronization

Abstract: We study a way to set the natural frequency of a newly added oscillator in a growing network to enhance synchronization. Population growth is one of the typical features of many oscillator systems for which synchronization is required to perform their functions properly. Despite this significance, little has been known about synchronization in growing systems. We suggest effective growing schemes to enhance synchronization as the network grows under a predetermined rule. Specifically, we find that a method based on a link-wise order parameter outperforms that based on the conventional global order parameter. With simple solvable examples, we verify that the results coincide with intuitive expectations. The numerical results demonstrate that the approximate optimal values from the suggested method show a larger synchronization enhancement in comparison to other naive strategies. The results also show that our proposed approach outperforms others over a wide range of coupling strengths.