层间Hebbian塑性诱导多重网络中的一级相变
Interlayer Hebbian Plasticity Induces First-Order Transition in Multiplex Networks
摘要：
适应在自然和人工复杂系统的进化以及它们功能的决定中起着关键作用。在这里，我们调查的影响，自适应层间进程的层内同步复用网络。所考虑的适应机制由赫布学习规则支配，即，如果两个节点同相，则增强一对互连节点之间的链路权重。这种自适应耦合诱导一个不可逆的一阶过渡路线同步伴随着滞后。我们提供严格的分析预测的临界耦合强度的同步和去同步的发病，并验证我们所有的理论预测通过广泛的数值模拟。
英文摘要：
Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in multiplex networks. The considered adaptation mechanism is governed by a Hebbian learning rule, i.e., the link weight between a pair of interconnected nodes is enhanced if the two nodes are in phase. Such adaptive coupling induces an irreversible first-order transition route to synchronization accompanied with a hysteresis. We provide rigorous analytic predictions of the critical coupling strengths for the onset of synchronization and de-synchronization, and verify all our theoretical predictions by means of extensive numerical simulations.
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