Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In this Letter, we develop the master stability approach for a large class of adaptive networks. This approach allows for reducing the synchronization problem for adaptive networks to a low-dimensional system, by decoupling topological and dynamical properties. We show how the interplay between adaptivity and network structure gives rise to the formation of stability islands. Moreover, we report a desynchronization transition and the emergence of complex partial synchronization patterns induced by an increasing overall coupling strength. We illustrate our findings using adaptive networks of coupled phase oscillators and FitzHugh-Nagumo neurons with synaptic plasticity.

中文翻译：

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自适应网络中的去同步转换

自适应网络根据其动态状态随时间改变其连接性。尽管对结构静态网络中的同步进行了广泛研究，但对于自适应网络而言，此问题更具挑战性。在这封信中，我们为一大类自适应网络开发了主稳定性方法。通过解耦拓扑和动态属性，此方法可以将自适应网络的同步问题减少到低维系统。我们展示了适应性和网络结构之间的相互作用如何引起稳定岛的形成。此外，我们报告了失步过渡和复杂的部分同步模式的出现，该模式由整体耦合强度的增加引起。