STABLE PERIODIC-SOLUTIONS TO DISCRETE AND CONTINUUM ARRAYS OF WEAKLY COUPLED NONLINEAR OSCILLATORS
STABLE PERIODIC-SOLUTIONS TO DISCRETE AND CONTINUUM ARRAYS OF WEAKLY COUPLED NONLINEAR OSCILLATORS
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DOI：
10.1137/0152096
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发表时间：
1992-12-01
影响因子：
1.9
通讯作者：
ERMENTROUT, GB
中科院分区：
文献类型：
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作者：
ERMENTROUT, GB
分析了空间分布神经振荡器阵列周期解的存在性和稳定性。找到了保证锁相图轨道稳定的条件。这些条件允许解随着某些参数的变化而扩展。对于具有某些可微条件的连续体阵列，当某些相位梯度变为无界时，锁定丢失。数值方法表明，所得结果适用于实际的突触耦合振荡神经网络。特别是，即使神经元是相同的，通常也不能期望同步解。
The existence and stability of periodic solutions to spatially distributed arrays of neural oscillators is analyzed. Conditions are found that guarantee that phase-locked patterns are orbitally stable. These conditions allow the solutions to be extended as some parameter varies. For continuum arrays with some differentiability conditions, it is shown that locking is lost when certain phase gradients become unbounded. Numerical methods are used to show that the results apply to realistic synaptically coupled oscillating neural networks. In particular, it is shown that synchronized solutions cannot generally be expected even if the neurons are identical.