极限环振子网络中频率的规则和非规则调制
Regular and irregular modulation of frequencies in limit cycle oscillator networks
摘要：
微扰调频是极限环振荡器区别于相位振荡器的本质特征。研究了频率受振幅变化敏感调制的全同极限环振子网络，证明了其频率可持续地取分布值。我们在网络中观察到两个复杂的现象：以规则的间隔平稳分布的频率和连续的不规则频率调制。在分析中，我们揭示了频率分布的机制，并展示了频率的敏感调制如何产生这些复杂的现象。我们还说明了网络的拓扑结构调节系统的行为。
英文摘要：
Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the change of their amplitudes, and demonstrated that the frequencies sustainably take distributed values. We observed two complex phenomena in the networks: stationarily distributed frequencies at a regular interval, and continuous irregular modulation of frequencies. In the analysis we reveal the mechanisms by which the frequencies are distributed, and show how the sensitive modulation of frequencies produces these complex phenomena. We also illustrate the topology of networks regulating the behaviors of the systems.
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