Park Youngmin, Ermentrout Bard
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA.
J Comput Neurosci. 2016 Jun;40(3):269-81. doi: 10.1007/s10827-016-0596-6. Epub 2016 Mar 5.
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.
我们扩展了弱耦合振子理论，以纳入缓慢变化的输入和参数。我们采用正则微扰和绝热近似相结合的方法，推导出一对振子之间相位差的方程。我们将此应用于简单的霍普夫振子，然后应用于一个生物物理模型。后者代表了一个神经元的行为，该神经元受到毒蕈碱电流的缓慢调制，例如在通过胆碱能激活的瞬态注意力过程中会发生的情况。我们的方法扩展并简化了久保林（《物理评论快报》，111, 214101, 2013）最近的工作，以包括耦合。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兴衰变化。
