分数阶时滞Willis 环脑动脉瘤系统的混沌分析
首发时间:2017-12-18
摘要:本文在分数阶Willis 环脑动脉瘤系统中加入时滞因素,构建出具有分数阶时滞的Willis环脑动脉瘤系统。弥补了已有的分数阶Willis 环脑动脉瘤系统中未能描述出的脑动脉瘤在实际治疗中会因药物和植入血流导向装置的治疗方法而产生时滞的缺憾。基于数值仿真的方法,重点考察时滞、阶数和系统参数对脑动脉瘤内血流的影响,并利用控制变量法对参数进行控制,从相关的分岔图等入手进行分析,研究了血流阻尼系数等对时滞的新系统的混沌产生的影响,揭示时滞系统随其参数变化所产生的丰富动力学行为并对基于植入血流导向装置治疗脑动脉瘤的方案给出了理论支持。
关键词: 分数阶时滞Willis 环脑动脉瘤系统 控制变量法 混沌分析
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Chaotic analysis of the fractional Willis aneurysm system with time-delay
Abstract:By introducing the time-delay factors in the existing fractional Willis aneurysm system, a new fractional Willis aneurysm system with time-delay was constructed in this paper. The research of this dissertation makes up for shortcomings of the existing fractional Willis aneurysm system. Which is the actual situation of time delay resulting from the treatment of drugs and the implantation of a blood -flow guiding device .Firstly, based on numerical simulation, the influence of time-delay parameter, order number and related parameters on blood flow in aneurysm areChaotic analysis of the fractional Willis aneurysm system with time-delay investigated. Then, using parameter variable method to control these parameters. By analysis the bifurcation diagrams and other diagrams related to these parameters with the knowledge of chaotic dynamics. The influence of the coefficients especially the coefficient of blood flaw dampening coefficient on the chaos behaviours of the fractional Willis aneurysm system with time-delay would be well known in this paper. Finally. It reveals that dynamic behaviours of the new system would change with its parameter changes and gives theoretical support for the treatment of the Willis aneurysm based on the implanted flow-oriented device.
Keywords: Fractional Willis Aneurysm System With Time-delay Control various methods Chaotic analysis
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分数阶时滞Willis 环脑动脉瘤系统的混沌分析
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