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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、Poincar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.
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关键词:
- 时滞 /
- 分数阶 /
- Willis环脑动脉血管瘤系统 /
- 混沌控制
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[14] Gu Y F, Xiao J 2014 Acta Phys. Sin. 63 160501 (in Chinese) [古元凤, 肖剑 2014 物理学报 63 160501]
[15] Li Y M, Yu S 2008 J. Biomath. 23 235 (in Chinese) [李医民, 于霜 2008 生物数学学报 23 235]
[16] Sun M H 2016 M. S. Thesis (Chongqing: University of Chongqing) (in Chinese) [孙梦晗 2016 硕士学位论文 (重庆: 重庆大学)]
[17] Gao F, Li T, Tong H Q, Ou Z L 2016 Acta Phys. Sin. 65 230502 (in Chinese) [高飞, 李腾, 童恒庆, 欧卓玲 2016 物理学报 65 230502]
[18] Lu K Q, Liu J X 2009 Physics 38 453 (in Chinese) [陆坤权, 刘寄星 2009 物理 38 453]
[19] Zhu K Q 2009 Mech. Pract. 31 104 (in Chinese) [朱克勤 2009 力学与实践 31 104]
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[22] Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 物理学报 62 018901]
[23] Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 物理学报 62 060201]
[24] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) p41
[25] Huo R, Wang X L, Wu G R 2014 J. Inner Mongolia Agric. Univ. (Nat. Sci. Edn.) 35 167 (in Chinese) [霍冉, 王晓丽, 吴国荣 2014 内蒙古农业大学学报 35 167]
[26] Hu J, Lu G, Zhang S, Zhao L 2015 Commun. Nonlinear Sci. 20 905
[27] Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. 15 2178
[28] Diethelm K, Neville F 2002 Nonlinear Dynam. 29 3
[29] Guan M, Shi H, Zhang G 2017 Chin. J. Cerebrovasc Dis. 14 46 (in Chinese) [关明浩, 史怀璋, 张广 2017 中国脑血管病杂志 14 46]
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[1] Lan Q 2015 Chin. J. Neurosurg. 31 541 (in Chinese) [兰青 2015 中华神经外科杂志 31 541]
[2] Liang S K, Jiang C H 2016 Chin. J. Neurosurg. 32 1071 (in Chinese) [梁士凯, 姜除寒 2016 中华神经外科杂志 32 1071]
[3] Liu A H 2017 Chin. J. Stroke 12 850 (in Chinese) [刘爱华 2017 中国卒中杂志 12 850]
[4] Fiorella D, Woo H H, Albuquerque F C, Nelson P K 2008 Neurosurgery 62 1115
[5] Liu J, Jing L K, Wang C, Paliwal N, Wang S Z, Zhang Y, Xiang J P, Siddiqui A H, Meng H, Yang X J 2016 J. Neurointerv. Surg. 8 1140
[6] Zhang Y, Yang X J 2016 Chin. J. Cerebrovasc. Dis. 7 372 (in Chinese) [张莹, 杨新健 2016 中国脑血管病杂志 7 372]
[7] Radaelli A G, Augsburger L, Cebral J R, Ohta M, Rufenacht D A, Balossino R, Benndorf G, Hose D R, Marzo A, Metcalfe R, Mortier P, Mut F, Reymond P, Socci L, Verhegghe B, Frangi A F 2008 J. Bio. 41 2069
[8] Connolly J E S, Rabinstein A A, Carhuapoma J R, Derdeyn C P, Dion J, Higashida R T, Hoh B L, Kirkness C J, Naidech A M, Ogilvy C S, Patel A B, Thompson B G, Vespa P, Council A H A S, Int C C R, Nursing C C, Anesthes C C S, Cardiology C C 2012 Stroke 43 1711
[9] Gonzalez C F, Cho Y I, Ortega H V, Moret J 1992 Am. J. Neuroradiol. 13 181
[10] Dai X, Qiao A K 2016 J. Med. Biomech. 31 461 (in Chinese) [戴璇, 乔爱科 2016 医用生物力学 31 461]
[11] Austin G 1971 Math. Biosci. 11 163
[12] Cao J D, Liu T Y 1993 J. Biomath. 8 9 (in Chinese) [曹进德, 刘天一 1993 生物数学学报 8 9]
[13] Yang C H, Zhu S M 2003 Acta Sci. Nat. Univ. Sunyatseni 43 1 (in Chinese) [杨翠红, 朱思铭 2003 中山大学学报(自然科学版) 43 1]
[14] Gu Y F, Xiao J 2014 Acta Phys. Sin. 63 160501 (in Chinese) [古元凤, 肖剑 2014 物理学报 63 160501]
[15] Li Y M, Yu S 2008 J. Biomath. 23 235 (in Chinese) [李医民, 于霜 2008 生物数学学报 23 235]
[16] Sun M H 2016 M. S. Thesis (Chongqing: University of Chongqing) (in Chinese) [孙梦晗 2016 硕士学位论文 (重庆: 重庆大学)]
[17] Gao F, Li T, Tong H Q, Ou Z L 2016 Acta Phys. Sin. 65 230502 (in Chinese) [高飞, 李腾, 童恒庆, 欧卓玲 2016 物理学报 65 230502]
[18] Lu K Q, Liu J X 2009 Physics 38 453 (in Chinese) [陆坤权, 刘寄星 2009 物理 38 453]
[19] Zhu K Q 2009 Mech. Pract. 31 104 (in Chinese) [朱克勤 2009 力学与实践 31 104]
[20] Ahmed E, El-Sayed A M A, El-Saka H A A 2007 J. Math. Anal. Appl. 325 542
[21] Dokoumetzidis A, Macheras P 2009 J. Pharmacokinet. Pharmacodyn. 36 165
[22] Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 物理学报 62 018901]
[23] Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 物理学报 62 060201]
[24] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) p41
[25] Huo R, Wang X L, Wu G R 2014 J. Inner Mongolia Agric. Univ. (Nat. Sci. Edn.) 35 167 (in Chinese) [霍冉, 王晓丽, 吴国荣 2014 内蒙古农业大学学报 35 167]
[26] Hu J, Lu G, Zhang S, Zhao L 2015 Commun. Nonlinear Sci. 20 905
[27] Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. 15 2178
[28] Diethelm K, Neville F 2002 Nonlinear Dynam. 29 3
[29] Guan M, Shi H, Zhang G 2017 Chin. J. Cerebrovasc Dis. 14 46 (in Chinese) [关明浩, 史怀璋, 张广 2017 中国脑血管病杂志 14 46]
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