Willis环状脑动脉瘤的生物数学模型的周期解

PERIODIC SOLUTIONS IN THE BIOMATHEMATICAL MODEL OF ANEURYSM OF CIRCLE OF WILLIS

本文运用扭转映射的不动点定理,通过Poincare'映射,在(μ/2)+((β~2)/(4a))<1的条件下,证明了Willis环状脑动脉瘤生物数学模型 +μ+αx-βx^2+γx^3=Fcosωt(其中μ,α,β,γ,F,ω都是正常数)至少存在一个(2π)/ω周期解。

In this paper, using Fixed points theorem of twist map, the author proves that the biomathematical model of aneurysm of circle of Willis: +μ+ax-βx^2+γx^3=Fcosωt (where μ,α,β,γ,F,ω are positive constant). There is at least one (2π)/ω-periodic solution under condition: μ/2+β~/(4γ)<1 by Poincare' map.