具有延迟控制的异质成核在自适应动态网络中
Delay-Controlled Heterogeneous Nucleation in Adaptive Dynamical Networks
AI总结：
研究揭示了具有连接延迟的有限大小自适应网络中异质成核的两种形式，通过单步和多步相变实现全局同步，并分析了延迟和自然频率分布对相变性质的影响。
摘要：
相变是解释广泛自然和工程系统中相互作用单元集体动力学突发或定性变化的基本机制。在动态网络中，此类相变导致耦合元素协调行为的重大重组。在自适应动态网络中，连接性动态地响应节点状态而演变，导致结构和动态的共进化。本文报告了两种不同的异质成核形式，导致有限大小自适应网络中向全局同步的单步和多步相变。我们证明相变的性质由延迟的存在和大小以及自然频率分布类别共同决定。使用集体坐标框架，我们开发了聚类动力学的均场描述，并推导了双聚类状态存在的解析上界条件，与数值模拟结果高度一致。此外，我们将分析扩展到具有分布式延迟的系统，并获得相应的解析条件。我们的结果为理解具有时间延迟相互作用的自适应网络中的同步相变提供了理论框架。
英文摘要：
Phase transitions constitute fundamental mechanisms underlying abrupt or qualitative changes in the collective dynamics of interacting units across a wide range of natural and engineered systems. In dynamical networks, such transitions lead to significant reorganization in the coordinated behavior of coupled elements. In adaptive dynamical networks, the connectivity evolves dynamically in response to the states of the nodes, resulting in a coevolution of structure and dynamics. In this work, we report two distinct forms of heterogeneous nucleation that give rise to single-step and multi-step phase transitions toward global synchronization in finite-size adaptive networks with connection delays. We demonstrate that the nature of the nucleation transition is governed by both the presence and magnitude of the delay, as well as the class of natural frequency distribution. Using a collective coordinate framework, we develop a mean-field description of cluster dynamics and derive an analytical upper bound condition for the existence of two-cluster states, which shows excellent agreement with numerical simulations. Furthermore, we extend the analysis to systems with distributed delays and obtain corresponding analytical conditions. Our results provide a theoretical framework for understanding synchronization transitions in adaptive networks with time-delayed interactions.
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