Coutts Emma J, Lord Gabriel J
African Institute for Mathematical Sciences, Cape Town, Western Cape, South Africa.
J Comput Neurosci. 2013 Apr;34(2):245-57. doi: 10.1007/s10827-012-0418-4. Epub 2012 Aug 16.
We study the effects of noise in two models of spiny dendrites. Through the introduction of different types of noise to both the Spike-diffuse-spike (SDS) and Baer-Rinzel (BR) models we investigate the change in behaviour of the travelling wave solution present in both deterministic systems, as noise intensity increases. We show that the speed of wave propagation in both the SDS and BR models respectively differs as the noise intensity in the spine heads increases. In contrast the cable is very robust to noise and as such the speed shows very little variation from the deterministic system. We introduce a space-dependent spine density, ρ(x), to the original Baer-Rinzel model and show how this modified model can mimic behaviour (under influence of noise) of both original systems, through variation of one parameter. We also show that the correlation time and length scales of the noise can enhance propagation of travelling wave solutions where the white noise dominates the underlying signal and produces noise induced phenomena.
我们研究了噪声在两种棘状树突模型中的影响。通过向“尖峰 - 扩散 - 尖峰”（SDS）模型和贝尔 - 林泽尔（BR）模型引入不同类型的噪声，我们研究了随着噪声强度增加，两个确定性系统中存在的行波解的行为变化。我们表明，随着棘突头部噪声强度的增加，SDS模型和BR模型中波的传播速度分别不同。相比之下，电缆对噪声非常鲁棒，因此速度与确定性系统相比变化很小。我们在原始的贝尔 - 林泽尔模型中引入了与空间相关的棘突密度ρ(x)，并展示了这个修改后的模型如何通过改变一个参数来模拟两个原始系统（在噪声影响下）的行为。我们还表明，噪声的相关时间和长度尺度可以增强行波解的传播，其中白噪声主导基础信号并产生噪声诱导现象。
