A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators
A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators
复制标题
DOI：
10.1007/s004220050501
复制
发表时间：
1999-01-01
影响因子：
1.9
通讯作者：
Byrne, JH
中科院分区：
文献类型：
--
作者：
Dror, R;Canavier, CC;Byrne, JH
Canavier等人（1997）使用单个振荡器的相位响应曲线（PRC）来表征N振荡器环形网络的锁相夹带的可能模式。我们扩展这项工作，通过开发一个数学标准，以确定这样的模式的基础上PRCs的局部稳定性。我们的方法并不假设对称性;振子和它们的连接都不需要相同。为了使用这些技术来预测模式并确定它们的稳定性，人们只需要通过实验或计算模型来确定环中每个振荡器的PRC。我们表明，网络的稳定性不能通过简单地测试每个振荡器的能力，夹带下一个。稳定性取决于环中神经元的数量、模式的类型以及每个PRC在相应神经元的夹带点处的斜率。我们还描述了简单的标准，这是必要的或足够的稳定性，并检查这些结果的影响。
Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes of phase-locked entrainment of an N-oscillator ring network. We extend this work by developing a mathematical criterion to determine the local stability of such a mode based on the PRCs. Our method does not assume symmetry; neither the oscillators nor their connections need be identical. To use these techniques for predicting modes and determining their stability, one need only determine the PRC of each oscillator in the ring either experimentally or from a computational model. We show that network stability cannot be determined by simply testing the ability of each oscillator to entrain the next. Stability depends on the number of neurons in the ring, the type of mode, and the slope of each PRC at the point of entrainment of the respective neuron. We also describe simple criteria which are either necessary or sufficient for stability and examine the implications of these results.