发表机构
Humboldt-Universität zu Berlin; Potsdam Institute for Climate Impact Research; University of Exeter; Southeast University; University College Cork（柏林洪堡大学; 波茨坦气候影响研究所; 埃克塞特大学; 东南大学; 科克大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究自适应延迟耦合相位振荡器中的频率爆发现象，发现频率失谐被量化为整数个自适应频率，并通过快慢分析揭示其机制，证明该现象在有限参数区域内稳健存在。
AI 中文摘要
我们报道了具有自适应和延迟耦合的相位振荡器系统中的频率爆发振荡。耦合强度的自适应被认为是缓慢的，并且依赖于振荡器之间的相位差。我们发现，由于自适应、集体动力学和时间延迟的联合链条，系统稳健地达到一种状态，在该状态下振荡器的频率近乎同步，但被整数个小的自适应频率所失谐。我们证明，这种失谐的量化是由交替的慢速和快速转变引起的。此外，观察到的运动呈现瞬时频率爆发的形式，每次爆发中的尖峰数量对应于失谐的量化水平。我们对该现象进行了快慢分析，并解释了爆发产生的机制。我们的研究结果表明，这些频率爆发振荡是稳健的，并在有限的参数区域内稳定存在。
英文摘要
We report on frequency bursting oscillations in a system of phase oscillators with adaptive and delayed coupling. Adaptation of the coupling strengths is considered slow and depends on the phase shift between the oscillators. We find due to the combined chain of adaptation, collective dynamics, and time delays, the system robustly achieves a state in which the oscillator's frequencies are nearly synchronized but detuned by an integer number of small adaptation frequencies. We demonstrate that this quantization of the detuning is caused by alternating slow and fast transitions. Moreover, the observed motions take the form of bursts of instantaneous frequency, and the number of spikes in each burst corresponds to the quantization level of the detuning. We provide a fast-slow analysis of this phenomenon and explain the mechanisms behind the emergence of bursts. Our findings indicate that these frequency bursting oscillations are robust and exist stably within finite parameter regions.
Comments20 pages, 7 figures
