具有惯性的常规库莫特网络中的时滞动力学：多稳定性、行波、奇点状态以及过渡到癫痫样活动
Time-Delayed Dynamics in Regular Kuramoto Networks with Inertia: Multistability, Traveling Waves, Chimera States, and Transitions to Seizure-Like Activity
AI总结：
研究探讨了惯性与时间延迟对常规转子网络同步动力学的影响，揭示其多稳定性、行波、奇点状态及癫痫样活动的形成机制。
摘要：
本研究探讨了惯性与时间延迟在常规转子网络中的复杂相互作用，基于第二阶库莫特模型框架。通过结合分析和数值方法，我们证明内在时间延迟——源于有限信息传输速度——诱导完全同步相锁状态的多稳定性。与无惯性系统不同，惯性会破坏这些相锁状态，减少其吸引盆地，并在特定惯性范围内产生非线性相锁动力学。此外，我们显示时间延迟促进湍流奇点状态的出现，而惯性增强其空间范围。值得注意的是，惯性与时间延迟的共同影响产生出类似于部分癫痫发作的动态模式。这些发现通过揭示惯性与时间延迟如何根本重塑常规转子网络的稳定性与动力学，为同步现象提供了新的见解，并对神经元建模和其他复杂系统具有更广泛的意义。
英文摘要：
This study examines the complex interplay between inertia and time delay in regular rotor networks within the framework of the second-order Kuramoto model. By combining analytical and numerical methods, we demonstrate that intrinsic time delays -- arising from finite information transmission speeds - induce multistability among fully synchronized phase-locked states. Unlike systems without inertia, the presence of inertia destabilizes these phase-locked states, reduces their basin of attraction, and gives rise to nonlinear phase-locked dynamics over specific inertia ranges. In addition, we show that time delays promote the emergence of turbulent chimera states, while inertia enhances their spatial extent. Notably, the combined influence of inertia and time delay produces dynamic patterns reminiscent of partial epileptic seizures. These findings provide new insights into synchronization phenomena by revealing how inertia and time delay fundamentally reshape the stability and dynamics of regular rotor networks, with broader implications for neuronal modeling and other complex systems.
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