Coombes S, Bressloff P C
Nonlinear and Complex Systems Group, Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Aug;60(2 Pt B):2086-96. doi: 10.1103/physreve.60.2086.
An analysis of mode-locked solutions that may arise in periodically forced integrate-and-fire (IF) neural oscillators is introduced based upon a firing map formulation of the dynamics. A q:p mode-locked solution is identified with a spike train in which p firing events occur in a period qDelta, where Delta is the forcing period. A linear stability analysis of the map of firing times around such solutions allows the determination of the Arnold tongue structure for regions in parameter space where stable solutions exist. The analysis is verified against direct numerical simulations for both a sinusoidally forced IF system and one in which a periodic sequence of spikes is used to induce a biologically realistic synaptic input current. This approach is extended to the case of two synaptically coupled IF oscillators, showing that mode-locked states can exist for some self-consistently determined common period of repetitive firing. Numerical simulations show that such solutions have a bursting structure where regions of spiking activity are interspersed with quiescent periods before repeating. The influence of the synaptic current upon the Arnold tongue structure is explored in the regime of weak coupling.
基于动力学的发放映射公式，对周期性强迫积分发放（IF）神经振荡器中可能出现的锁模解进行了分析。q:p锁模解与一种发放序列相关，其中在qΔ的周期内发生p次发放事件，这里的Δ是强迫周期。围绕此类解对发放时间映射进行线性稳定性分析，可以确定参数空间中存在稳定解的区域的阿诺德舌结构。针对正弦强迫IF系统以及使用周期性脉冲序列来诱导生物现实突触输入电流的系统，通过直接数值模拟验证了该分析。此方法扩展到两个突触耦合IF振荡器的情况，表明对于某些自洽确定的重复发放共同周期，可以存在锁模状态。数值模拟表明，此类解具有一种爆发结构，其中发放活动区域在重复之前穿插着静止期。在弱耦合 regime 中探讨了突触电流对阿诺德舌结构的影响。
