Weakly coupled oscillators in a slowly varying world
Weakly coupled oscillators in a slowly varying world
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缓慢变化的世界中的弱耦合振荡器
DOI：
10.1007/s10827-016-0596-6
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发表时间：
2016
影响因子：
1.2
通讯作者：
B. Ermentrout
中科院分区：
文献类型：
--
作者：
Youngmin Park;B. Ermentrout
我们扩展了弱耦合振荡器的理论，以纳入缓慢变化的输入和参数。我们采用规则扰动和绝热近似的组合来推导一对振荡器之间的相位差方程。我们将其应用于简单的 Hopf 振荡器，然后应用于生物物理模型。后者代表神经元的行为，该神经元受到毒蕈碱电流的缓慢调制，例如通过胆碱能激活在短暂注意力期间发生的情况。我们的方法扩展并简化了 Kurebayashi (Physical Review Letters, 111, 214101, 2013) 最近的工作，包括耦合。我们将该方法应用于全对全网络，并表明调制神经元的同步性存在增减。
We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Review Letters, 111, 214101, 2013) to include coupling. We apply the method to an all-to-all network and show that there is a waxing and waning of synchrony of modulated neurons.