基于药物作用的Willis环脑动脉瘤模型的混沌分析

全部作者: 孙梦晗,肖剑,董海亮,张晓青
作者单位: 重庆大学数学与统计学院
摘 要: 通过引入降压药物激励项函数,构造了一个新的Willis环脑动脉瘤数学模型。从混沌吸引子的存在性、Lyapunov指数谱、Poincaré截面,对该脑动脉瘤模型进行动力学分析。基于数值仿真,分析各个参量值对脑动脉瘤模型混沌的影响。最后,基于对相图和Poincaré截面的分析,证明了降压药物有助于脑动脉瘤病情的控制。
关 键 词: 运筹学;脑动脉瘤;动力学分析;Lyapunov指数谱;降压药物
Title: Analysis of the circle of Willis chaotic system based on pharmaceuticals
Author: SUN Menghan, XIAO Jian, DONG Hailiang, ZHANG Xiaoqing
Organization: School of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Abstract: A new model of the circle of Willis chaotic system is constructed through the introduction of antihypertensive drugs’ inspirit function. Phase portraits indicate that the system contains the chaotic attractor. The chaotic complex dynamic characteristics of the new system are analyzed, including the existence of chaotic attractor, the Lyapunov exponents and the Poincaré section. The influence of each parameter of the new Willis chaotic system on the system is investigated based on the numerical simulation. Finally, the effective control of antihypertensive drugs for cerebral aneurysm is investigated by the analysis of the phase portraits and Poincaré section.
Key words: operational research; cerebral aneurysm; dynamic analysis; Lyapunov exponents; antihypertensive drug
发表期数: 2016年4月第7期
引用格式: 孙梦晗,肖剑,董海亮,等. 基于药物作用的Willis环脑动脉瘤模型的混沌分析[J]. 中国科技论文在线精品论文,2016,9(7):640-649.
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