分数阶Willis环脑迟发性动脉瘤时滞系统混沌分析  

Chaotic analysis of fractional Willis delayed aneurysm system

作　　者：高飞[1] 胡道楠 童恒庆[1] 王传美[1] Gao Fei;Hu Dao-Nan;Tong Heng-Qing;Wang Chuan-Mei(School of Science,Wuhan University of Technology,Wuhan 430070,Chin)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《物理学报》2018年第15期275-285,共11页Acta Physica Sinica

基　　金：国家自然科学基金重大研究计划(批准号:91324201);中央高校基本科研业务费(批准号:2018IB017);湖北省自然科学基金(批准号:2014CFB865);教育部人文社科青年基金项目(批准号:14YJCZH143)资助的课题~~

摘　　要：在脑血动脉瘤的临床研究中,Willis环脑动脉血管瘤系统(Willis aneurysm system,WAS)起着重要作用,分数阶WAS尽管能进一步加深该系统的机理刻画,但是不能描述原因不明的迟发性动脉瘤.鉴于此,本文提出分数阶Willis环脑迟发性动脉瘤时滞系统(fractional Willis aneurysm system with time-delay,FWASTD)并验证了其有效性;利用时间序列图、相图、Poincaré截面等证实了FWASTD的混沌特性;研究时滞对于系统的重要生理参量的影响,发现了血流阻力系数在时滞状态下对系统稳定的重要性;根据分数阶时滞系统的稳定性理论,设计相应线性控制器,对FWASTD进行了有效控制,同时也探讨了时滞系统的自同步控制.本文完善了脑动脉瘤系统的理论基础.The dynamic system of Willis aneurysm（WAS） has played an important role in theoretical and clinical research of cerebral aneurysms. Fractional differential is an effective mathematical tool that can describe the cerebral aneurysm system accurately and profoundly. However, the existing fractional Willis aneurysm system（FWAS） cannot describe the delayed aneurysm rupture of unknown cause in reality. Therefore, by introducing the time-delay factors into the existing fractional Willis aneurysm system as a rational extension, a new fractional Willis aneurysm system with time-delay（FWASTD） is proposed in this paper.First, FWASTD is introduced in the context, and the comparison of time sequences map between FWAS and FWASTD proves that FWASTD is feasible in the depiction of time-delay situations. The bifurcation diagram and the largest Lyapunov exponent diagram as well as the phase diagram of fractional order also confirm the chaotic characteristics of the FWASTD.Then, the classical analysis methods in chaotic dynamics, such as time series diagram, phase diagram and Poincarésection are used to analyze FWASTD in detail. When studying the diagrams of time-delay factors for the important physiological parameters of the system, we find that blood flow resistance coefficient can exert a remarkable effect on the system stability under time-delay. Besides, the experimental results show that the FWASTD becomes stable with the increase of blood flow resistance under a certain condition. Usually, promoting thrombosis is a kind of adjunctive therapy in clinic for cerebral aneurysm. The results of this part can accord with the treatment in clinic and has great significance in clinical diagnosis.Finally, as the chaotic state of the time-delay system indicates that cerebral aneurysm is in a dangerous situation,the primary task of the control for this new system is to achieve stability rather than synchronization. The stability theory of fractional time-delayed system is adopted in a strict proof of the uniqueness of soluti

关 键 词：时滞 分数阶 Willis环脑动脉血管瘤系统 混沌控制 

分 类 号：O415.5[理学—理论物理] R743.3[理学—物理]