物理学报2016，Vol.65Issue(23)：230502-1-230502-11,11.DOI:10.7498/aps.65.230502
分数阶Willis环脑动脉瘤系统的混沌动力学分析与控制∗
Chaotic dynamics of the fractional Willis aneurysm system and its control
摘要
Abstract
The Willis aneurysm system has some limitations in the description of the complex hemodynamic mechanism of blood with viscoelasticity. The fractional calculus has been used to depict some complex and disordered processes in organisms. Thus, we propose a fractional Willis aneurysm system (FWAS) byusing the Caputo fractional differential and its theory in the present article. <br> Firstly, the existence and uniqueness of solution for FWAS are investigated theoretically. Then, we prove that the FWAS has a chaotic characteristic by analyzing the phase portraits and Poincaré section, and it is a rational extension of its integer order form. We investigate the influences of pulse pressure and fractional order on the FWAS by means of bifurcation diagram and period doubling bifurcation. The results show that small changes of pulse pressure and fractional order canlead to a remarkable effect on the motion state of the FWAS. <br> As the chaotic FWAS indicates that the brain blood flow is unstable, and the cerebral aneurysms are more likely to rupture in a very chaotic velocity field. Therefore we use two methods to control the chaotic FWAS. One is to design a suitable controller based on the stability theorem of fractional nonlinear non-autonomous system, and the other is to use a pulse control by taking the inspirit function of drug as impulse function. The numerical simulations show that the proposed two methods can control the blood flow velocity and speed up the periodic fluctuation within a small range, which shows that the cerebral aneurysm is not easy to rupture. <br> The results obtained in this paper display that the fractional differential is a feasible method to characterize the Willis aneurysm system. The theoretical results in our article can provide some theoretical guidance for controlling and utilizing the actual FWAS system.关键词
分数阶Willis环脑动脉瘤系统/分数阶Caputo微分/Poincaré截面/混沌控制Key words
fractional Willis aneurysm system/Caputo fractional differential/Poincaré section/chaos control引用本文复制引用
高飞,李腾,童恒庆,欧卓玲..分数阶Willis环脑动脉瘤系统的混沌动力学分析与控制∗[J].物理学报,2016,65(23):230502-1-230502-11,11.基金项目
国家自然科学基金重大研究计划(批准号:91324201)和湖北省自然科学基金(批准号:2014CFB865)资助的课题 （批准号:91324201）
