Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan.
Math Biosci Eng. 2014 Feb;11(1):125-38. doi: 10.3934/mbe.2014.11.125.
To elucidate how a biological rhythm is regulated, the extended (three-dimensional) Bonhoeffer-van der Pol or FitzHugh-Nagumo equations are employed to investigate the dynamics of a population of neuronal oscillators globally coupled through a common buffer (mean field). Interesting phenomena, such as extraordinarily slow phase-locked oscillations (compared to the natural period of each neuronal oscillator) and the death of all oscillations, are observed. We demonstrate that the slow synchronization is due mainly to the existence of "fast" oscillators. Additionally, we examine the effect of noise on the synchronization and variability of the interspike intervals. Peculiar phenomena, such as noise-induced acceleration and deceleration, are observed. The results herein suggest that very small noise may significantly influence a biological rhythm.
为了阐明生物节律是如何调节的，采用扩展（三维）邦霍夫-范德波尔或菲茨休-纳戈莫诺方程来研究通过公共缓冲器（平均场）全局耦合的神经元振荡器群体的动力学。观察到有趣的现象，例如非常缓慢的锁相振荡（与每个神经元振荡器的自然周期相比）和所有振荡的死亡。我们证明，缓慢的同步主要是由于“快速”振荡器的存在。此外，我们还研究了噪声对峰间间隔同步和可变性的影响。观察到一些奇特的现象，如噪声诱导的加速和减速。本文的结果表明，非常小的噪声可能会对生物节律产生重大影响。
