Tass P
Department of Neurology, Heinrich-Heine-University, Düsseldorf, Germany.
J Biol Phys. 1997 Mar;23(1):21-66. doi: 10.1023/A:1004990707739.
From a theoretical point of view we investigate cortical activity patterns causing dynamic visual hallucinations. For this reason we analyze an oscillatory instability of the dynamics ofthe activator-inhibitor model of Ermentrout and Cowan.Such an oscillatory instability occurs as a result of several disease mechanisms.We explicitly derive the order parameter equation. By means of the averaging theorem, we obtain the averaged order parameter equation.The latter enables us to determine stable and unstable bifurcating cortical activity patterns analytically in lowest order.Depending on model parameters as well as on initial conditions two types of cortical activity patterns occur: travelling waves and 'blinking rolls', i.e.standing waves oscillating with the same frequency and with a phase shift of π/2. In contrast to cortical activitypatterns caused by non-oscillatory instabilitiesanalyzed by Ermentrout and Cowan and by the author the travelling waves and the blinking rolls lead to a variety of dynamic visual hallucinations which are discussed indetail.
从理论角度出发，我们研究导致动态视幻觉的皮层活动模式。因此，我们分析了厄门特劳特和考恩的激活-抑制模型动力学的振荡不稳定性。这种振荡不稳定性是由多种疾病机制导致的。我们明确推导了序参量方程。借助平均定理，我们得到了平均序参量方程。后者使我们能够以最低阶解析地确定稳定和不稳定的分岔皮层活动模式。根据模型参数以及初始条件，会出现两种类型的皮层活动模式：行波和“闪烁波卷”，即具有相同频率且相位偏移为π/2的驻波。与厄门特劳特、考恩以及作者所分析的由非振荡不稳定性引起的皮层活动模式不同，行波和闪烁波卷会导致各种动态视幻觉，我们将对此进行详细讨论。
