Maïna I, Tabi C B, Ekobena Fouda H P, Mohamadou A, Kofané T C
Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon.
Department of Physics, Faculty of Science, University of Maroua, P. O. Box 814, Maroua, Cameroon.
Chaos. 2015 Apr;25(4):043118. doi: 10.1063/1.4919077.
We exclusively analyze the condition for modulated waves to emerge in two ephaptically coupled nerve fibers. Through the multiple scale expansion, it is shown that a set of coupled cable-like Hodgkin-Huxley equations can be reduced to a single differential-difference nonlinear equation. The standard approach of linear stability analysis of a plane wave is used to predict regions of parameters where nonlinear structures can be observed. Instability features are shown to be importantly controlled not only by the ephaptic coupling parameter, but also by the discreteness parameter. Numerical simulations, to verify our analytical predictions, are performed, and we explore the longtime dynamics of slightly perturbed plane waves in the coupled nerve fibers. On initially exciting only one fiber, quasi-perfect interneuronal communication is discussed along with the possibility of recruiting damaged or non-myelinated nerve fibers, by myelinated ones, into conduction.
我们专门分析了调制波在两条电突触耦合神经纤维中出现的条件。通过多尺度展开，结果表明一组耦合的类电缆霍奇金-赫胥黎方程可以简化为一个单一的微分-差分非线性方程。采用平面波线性稳定性分析的标准方法来预测可观察到非线性结构的参数区域。结果表明，不稳定性特征不仅受到电突触耦合参数的重要控制，还受到离散参数的重要控制。为了验证我们的分析预测，进行了数值模拟，并且我们探索了耦合神经纤维中轻微扰动平面波的长期动力学。在最初仅激发一根纤维时，讨论了准完美的神经元间通信以及有髓神经纤维将受损或无髓神经纤维纳入传导的可能性。
