关于Frohlich电波模型的周期轨道的存在性

On the Existence of Periodic Orbit of Frhlich's Model for Brain Waves

关于Ｆｒｏｈｌｉｃｈ电波模型的周期轨道的存在性罗桂诗（暨南大学教学系５１０６３２，广州）摘要利用Ｈｏｐｆ分支理论对Ｆｒｏｈｌｉｃｈ建立的一个脑电波模型在三维空间中进行分析，推证出该系统前实存在周期轨道解．关键词：脑电波模型；周期轨道；存在性申回升线号...

The following Frohlich's model for brain waves is discussed under the assumption thatA, a, p,y and A are all positive constants:systgn (1). has two equilirium points: E_1 (0, 0, A), EZ(γ/aA, β/aA, A). By Hartman'slinearisation theorem, E1 is dearly a saddle point. Taking A as a parameter, then anapplication of Hopf's bifurcation theorem to (1), with E_2 as the new original, yields asufficient condition for the eds.toare of a periodic orbit of (1) in te neighbourhood ofequilirium E_2.