Kawahara T
Biol Cybern. 1980;39(1):37-43. doi: 10.1007/BF00336943.
A system of mutually coupled Van der Pol equations is derived from an extended version of the Wilson and Cowan model for the dynamics of a number of excitatory and inhibitory neural subsets. In the lowest order of approximation, interactions between excitatory and inhibitory subsets appear as linear elastic coupling, while those within and between excitatory and excitatory subsets appear as nonlinear frictional coupling. The case of two coupled oscillators is investigated by the method of averaging and the stability conditions for two mode oscillations are obtained. Internal resonance is also discussed briefly in the case of identical oscillators.
一个相互耦合的范德波尔方程组是从威尔逊和考恩模型的扩展版本推导而来的，该模型用于描述多个兴奋性和抑制性神经子集的动力学。在最低阶近似中，兴奋性和抑制性子集之间的相互作用表现为线性弹性耦合，而兴奋性和兴奋性子集内部以及它们之间的相互作用表现为非线性摩擦耦合。通过平均法研究了两个耦合振子的情况，并得到了双模振荡的稳定性条件。对于相同振子的情况，也简要讨论了内共振。
