标题： 具有约束条件的网络适应的多时间尺度动力学 显示英文标题

标题： Multiple Timescale Dynamics of Network Adaptation with Constraints

摘要： 自适应网络动态系统描述了节点上的动态量以及网络连接本身的动态共同演化。 对于许多节点的密集网络，产生的动态通常是高维的。 在这里，我们考虑受到网络适应约束的自适应动态系统：在渐近情况下，网络连接的自适应动态在可能的连接性的低维子集上演化。 这种维度降低可能是适应规则本身的固有特性，或者来自在不同于网络适应的时间尺度上起作用的额外动态机制。 我们说明了具有各种约束条件的网络适应如何影响Kuramoto振子网络的动态，并阐明了多时间尺度在塑造动态中的作用。 我们的结果揭示了为什么在一般高维的自适应网络动态系统中可能会期望有效的低维适应动态。 显示英文摘要

摘要： Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resulting dynamics are typically high-dimensional. Here we consider adaptive dynamical systems subject to constraints on network adaptation: Asymptotically, the adaptive dynamics of network connections evolve on a low-dimensional subset of possible connectivity. Such dimension reduction may be intrinsic to the adaptation rule or arise from an additional dynamical mechanism acting on a timescale distinct from that of network adaptation. We illustrate how network adaptation with various constraints influences the dynamics of Kuramoto oscillator networks and elucidate the role of multiple timescales in shaping the dynamics. Our results shed light on why one may expect effective low-dimensional adaptation dynamics in generally high-dimensional adaptive network dynamical systems.