具有多重和状态依赖时滞的相位振子网络：探索神经动力学中白质可塑性的框架
Phase oscillator networks with multiple and state-dependent delays: A framework for exploring white matter plasticity in neurodynamics
- University of Nottingham（诺丁汉大学）
- Istanbul Ticaret University（伊斯坦布尔商科大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出一个含多重和状态依赖时滞的相位振子网络框架，通过约化为时滞微分方程分析白质可塑性对神经动力学的影响，发现其可促进网络更连贯的行为。
中文摘要 AI 辅助
网络科学日益关注节点动力学如何影响涌现现象，如振荡、波、嵌合体和湍流。在由耦合常微分方程（ODEs）网络建模的振荡系统中，一种常见方法是将系统约化为相位变量。在理解网络时滞如何塑造涌现特性时，时滞通常被吸收进约化描述中作为相移。约化系统是一组常微分方程，会丢失关于完整时滞微分方程（DDE）系统的某些信息。我们采用一种限制较少的方法，考虑具有多重时滞的极限环振子网络，该网络可约化为时滞微分方程系统。这捕获了延迟耦合的效应，包括状态的共存和多稳定性。我们利用先前为更一般的时滞微分方程设置开发的工具，分析相位锁定态形式的相对平衡。这使我们能够使用对称分岔理论、线性稳定性分析以及数值模拟和延拓，探索具有空间依赖时滞的网络中的模式形成，包括在神经科学中的应用。在大脑动力学中，时滞由通信信号（动作电位）沿纤维（轴突）传播的速度决定。重要的是，这些时滞现在已知是状态依赖的，因为绝缘轴突的髓鞘（白质）是可塑的，并能响应神经元活动而改变。我们引入并分析了一个简单的现象学模型（在相位约化描述中），通过扩展为固定时滞开发的技术。我们的分析表明，白质可塑性可以驱动网络走向更连贯的行为。
英文摘要
Network science is increasingly focused on how node dynamics influence emergent phenomena such as oscillations, waves, chimeras, and turbulence. In oscillatory systems modeled by networks of coupled ordinary differential equations (ODEs), a common approach is to reduce the system to phase variables. When understanding how network delays shape emergent properties, the delays are often absorbed in the reduced description as a phase shift. The reduced system is a set of ODEs that loses some information about the full delay differential equation (DDE) system. We adopt a less restrictive approach and consider limit cycle oscillator networks with multiple delays that can be reduced to a DDE system. This captures the effects of delayed couplings, including coexistence and multistability of states. We analyze relative equilibria in the form of phase-locked states with tools previously developed for more general DDE settings. This allows us to explore patterning in networks with space-dependent delays, including in neuroscience, using symmetric bifurcation theory, linear stability analysis, and numerical simulations and continuation. In brain dynamics, time delays are determined by the speed of a communicating signal (action potential) along a fiber (axon). Importantly, these are now known to be state-dependent since the myelin (white matter) that insulates axons is plastic and can change in response to neuronal activity. A simple phenomenological model of this process (in the phase reduced description) is introduced and analyzed by extending techniques developed for fixed delays. Our analysis suggests that white matter plasticity can drive networks to more coherent behavior.
