Postnov D, Han S K, Kook H
Department of Physics, Chungbuk National University, Cheongju, Chungbuk 361-763, Korea.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Sep;60(3):2799-807. doi: 10.1103/physreve.60.2799.
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the in-phase synchronization and also that it is the only stable state in the weak-coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the sychronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak-coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis.
众所周知，两个极限环振荡之间的扩散耦合通常会导致同相同步，而且在弱耦合极限下这是唯一的稳定状态。然而，最近有研究表明，当极限环接近同宿分岔时，相同性质的耦合会导致独特的异相同步，这种情况尤其常出现在神经元振荡器中。在本文中，我们提出了一个使用修正范德波尔方程的简单物理模型，它展现了后一种类型的一般同步行为，并且在其中人们也可以很容易地观察到不同状态之间同步行为的变化。在弱耦合极限下，对异相机制进行了定性和定量分析。引入了一种一般形式的耦合，并利用分岔分析探索了广泛耦合参数范围内的同步行为，以构建相图。
