Please wait a minute...
Chin. Phys. B, 2019, Vol. 28(9): 090501    DOI: 10.1088/1674-1056/ab38a4
GENERAL Prev   Next  

Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system

Fei Gao(高飞), Wen-Qin Li(李文琴), Heng-Qing Tong(童恒庆), Xi-Ling Li(李喜玲)
School of Science, Wuhan University of Technology, Wuhan 430070, China
Abstract  

A new Willis aneurysm system is proposed, which contains the Atangana-Baleanu(AB) fractional derivative. we obtain the numerical solution of the Atangana-Baleanu fractional Willis aneurysm system (ABWAS) with the AB fractional integral and the predictor-corrector scheme. Moreover, we research the chaotic properties of ABWAS with phase diagrams and Poincare sections. The different values of pulse pressure and system order are used to evaluate and compare their effects on ABWAS. The simulations verify that the changes of pulse pressure and system order are the significant reason for ABWAS' states varying from chaotic to steady. In addition, compared with Caputo fractional WAS (FWAS), ABWAS shows less state that is chaotic. Furthermore, the results of bifurcation diagrams of blood flow damping coefficient and reciprocal heart rate show that the blood flow velocity tends to stabilize with the increase of blood flow damping coefficient or reciprocal heart rate, which is consistent with embolization therapy and drug therapy for clinical treatment of cerebral aneurysms. Finally, in view of the fact that ABWAS in chaotic state increases the possibility of rupture of cerebral aneurysms, a reasonable controller is designed to control ABWAS based on the stability theory. Compared with the control results of FWAS by the same method, the results show that the blood flow velocity in the ABWAS system varies in a smaller range. Therefore, the control effect of ABWAS is better and more stable. The new Willis aneurysm system with Atangana-Baleanu fractional derivative provides new information for the further study on treatment and control of brain aneurysms.

Keywords:  fractional Willis aneurysm system      Atangana-Baleanu fractional differential      Poincaré      section      chaos control  
Received:  23 April 2019      Revised:  14 June 2019      Accepted manuscript online: 
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: 

Project supported by the State Key Program of the National Natural Science of China (Grant No. 91324201), the Fundamental Research Funds for the Central Universities of China, the Self-determined and Innovative Research Funds of WUT, China (Grant No. 2018IB017), and the Natural Science Foundation of Hubei Province of China (Grant No. 2014CFB865).

Corresponding Authors:  Fei Gao     E-mail:  hgaofei@gmail.com

Cite this article: 

Fei Gao(高飞), Wen-Qin Li(李文琴), Heng-Qing Tong(童恒庆), Xi-Ling Li(李喜玲) Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system 2019 Chin. Phys. B 28 090501

[41] Wu Y F, Shen J, Huang Q H, Xiang J P, Meng H and Lu J M 2012 Acad. J. Second Mil. Med. Univ. 33 195199(in Chinese)
[1] Ji Q B, Zhou Y, Yang Z Q and Meng X Y 2015 Chin. Phys. Lett. 32 050501
[42] Liu X and Wen C 2018 Med. Philos. 39 3336(in Chinese)
[2] Wang X Y, Wang Y, Wang S W, Zhang Y Q and Wu X J 2018 Chin. Phys. B 27 110502
[3] Zhang R, Peng M, Zhang Z D and Bi Q S 2018 Chin. Phys. B 27 110501
[4] Sadasivan C, Fiorella D J, Woo H H and Lieber B B 2013 Ann. Biomed. Eng. 41 13471365
[5] Austin G 1971 Math. Biosci. 11 163172
[6] Liu T Y and Wan S D 1989 J. Biomath. 1 2128(in Chinese)
[7] Liu T Y and Li C X 1990 J. Yunnan Inst. Technol. 4 0108(in Chinese)
[8] Cao J D and Liu T Y 1993 J. Biomath. 2 0916(in Chinese)
[9] Yang C H and Zhu S M 2003 Acta Sci. Nat. Univ. Sunyatseni 42 0103(in Chinese)
[10] Feng C H 1998 J. Biomath. 13 6164(in Chinese)
[11] Nieto J J and Torres A 2000 Nonlinear Anal. 40 513521
[12] Li Y M and Yu S 2008 J. Biomath. 23 235238(in Chinese)
[13] Peng S H, Li D H, Su Z and Li H D 2010 Comput. Eng. Appl. 46 245248(in Chinese)
[14] Sun M H, Xiao J and Dong H L 2016 Highlights of Sciencepaper Online 9 640(in Chinese)
[15] Gao F, Li T, Tong H Q and Ou Z L 2016 Acta Phys.Sin. 65 5262(in Chinese)
[16] Atangana A 2015 Derivative with a new parameter:Theory, methods and applications (New York:Academic Press) pp. 73-150
[17] Sheikh N A, Ali F, Khan I and Saqib M 2018 Neural Comput. Appl. 30 18651875
[18] Caputo M and Fabrizio M 2015 Progr. Fract. Differ. Appl. 1 7385
[19] Saqib M, Ali F, Khan I, Sheikh N A, Jan S A A and Samiulhaq 2018 Alexandria Eng. J. 57 18491858
[20] Atangana A and Gómez-Aguilar J F 2017 Chaos, Solitons Fractals 102 285294
[21] Atangana A and Gómez-Aguilar J F 2017 Physica A 476 0114
[22] Atangana A and Baleanu D 2016 Therm. Sci. 20
[23] Gómez-Aguilar J F, Escobar-Jiménez R F, López-López M G and Alvarado-Martínez V M 2016 J. Electromagn. Waves. Appl. 30 19371952
[24] Bas E and Ozarslan R 2018 Chaos, Solitons Fractals 116 121125
[25] Owolabi K M 2018 Eur. Phys. J. Plus 133 15
[26] Coronel-Escamilla A, Gómez-Aguilar J, Baleanu D, Cérdova-Fraga T, Escobar-Jimónez R, Olivares-Peregrino V and Qurashi M 2017 Entropy 19 55
[27] Gómez-Aguilar J, Morales-Delgado V, Taneco-Hernández M, Baleanu D, Escobar-Jiménez R and Al Qurashi M 2016 Entropy 18 402
[28] Gómez-Aguilar J F, Atangana A and Morales-Delgado V F 2017 Int. J. Circuit Theory Appl. 45 15141533
[29] Kashif A A, Mukkarum H and Mirza M B 2017 Eur. Phys. J. Plus 132 439
[30] Sheikh N A, Ali F, Khan I, Gohar M and Saqib M 2017 Eur. Phys. J. Plus 132 540
[31] Asjad M I, Miraj F and Khan I 2018 Eur. Phys. J. Plus 133 224
[32] Sheikh N A, Ali F, Saqib M, Khan I, Jan S A A, Alshomrani A S and Alghamdi M S 2017 Results Phys. 7 789800
[33] Alqahtani R T 2016 J. Nonlinear. Sci. Appl. 9 36473654
[34] Atangana A 2017 Fractional operators with constant and variable order with application to geo-hydrology (New York:Academic Press) pp. 52-130
[35] Atangana A and Koca I 2016 Chaos, Solitons Fractals 89 447454
[36] Omar A A and Al-Smadi M 2018 Chaos, Solitons Fractals 117 161167
[37] Zhu K Q 2009 Mech.Pract. 31 104(in Chinese)
[38] Lu K Q and Liu J X 2009 Physics 38 453(in Chinese)
[39] Saif U, Muhammad A K and Muhammad F 2018 Eur. Phys. J. Plus 133 313
[40] Alkahtani B S T 2016 Chaos, Solitons Fractals 89 547551
[41] Wu Y F, Shen J, Huang Q H, Xiang J P, Meng H and Lu J M 2012 Acad. J. Second Mil. Med. Univ. 33 195199(in Chinese)
[42] Liu X and Wen C 2018 Med. Philos. 39 3336(in Chinese)
[1] Spontaneous emission of a moving atom in a waveguide of rectangular cross section
Jing Zeng(曾静), Jing Lu(卢竞), and Lan Zhou(周兰). Chin. Phys. B, 2023, 32(2): 020302.
[2] Direct measurement of an energy-dependent single-event-upset cross-section with time-of-flight method at CSNS
Biao Pei(裴标), Zhixin Tan(谭志新), Yongning He(贺永宁), Xiaolong Zhao(赵小龙), and Ruirui Fan(樊瑞睿). Chin. Phys. B, 2023, 32(2): 020705.
[3] High frequency doubling efficiency THz GaAs Schottky barrier diode based on inverted trapezoidal epitaxial cross-section structure
Xiaoyu Liu(刘晓宇), Yong Zhang(张勇), Haoran Wang(王皓冉), Haomiao Wei(魏浩淼),Jingtao Zhou(周静涛), Zhi Jin(金智), Yuehang Xu(徐跃杭), and Bo Yan(延波). Chin. Phys. B, 2023, 32(1): 017305.
[4] State-to-state integral cross sections and rate constants for the N+(3P)+HD→NH+/ND++D/H reaction: Accurate quantum dynamics studies
Hanghang Chen(陈航航), Zijiang Yang(杨紫江), and Maodu Chen(陈茂笃). Chin. Phys. B, 2022, 31(9): 098204.
[5] Effect of conical intersection of benzene on non-adiabatic dynamics
Duo-Duo Li(李多多) and Song Zhang(张嵩). Chin. Phys. B, 2022, 31(8): 083103.
[6] New experimental measurement of natSe(n, γ) cross section between 1 eV to 1 keV at the CSNS Back-n facility
Xin-Rong Hu(胡新荣), Long-Xiang Liu(刘龙祥), Wei Jiang(蒋伟), Jie Ren(任杰), Gong-Tao Fan(范功涛), Hong-Wei Wang(王宏伟), Xi-Guang Cao(曹喜光), Long-Long Song(宋龙龙), Ying-Du Liu(刘应都), Yue Zhang(张岳), Xin-Xiang Li(李鑫祥), Zi-Rui Hao(郝子锐), Pan Kuang(匡攀), Xiao-He Wang(王小鹤), Ji-Feng Hu(胡继峰), Bing Jiang(姜炳), De-Xin Wang(王德鑫), Suyalatu Zhang(张苏雅拉吐), Zhen-Dong An(安振东), Yu-Ting Wang(王玉廷), Chun-Wang Ma(马春旺), Jian-Jun He(何建军), Jun Su(苏俊), Li-Yong Zhang(张立勇), Yu-Xuan Yang(杨宇萱), Sheng Jin(金晟), and Kai-Jie Chen(陈开杰). Chin. Phys. B, 2022, 31(8): 080101.
[7] Integral cross sections for electron impact excitations of argon and carbon dioxide
Shu-Xing Wang(汪书兴) and Lin-Fan Zhu(朱林繁). Chin. Phys. B, 2022, 31(8): 083401.
[8] Elastic electron scattering with CH2Br2 and CCl2Br2: The role of the polarization effects
Xiaoli Zhao(赵小利) and Kedong Wang(王克栋). Chin. Phys. B, 2022, 31(8): 083402.
[9] Scaled radar cross section measurement method for lossy targets via dynamically matching reflection coefficients in THz band
Shuang Pang(逄爽), Yang Zeng(曾旸), Qi Yang(杨琪), Bin Deng(邓彬), and Hong-Qiang Wang(王宏强). Chin. Phys. B, 2022, 31(6): 068703.
[10] Measurement of 232Th (n,γ) cross section at the CSNS Back-n facility in the unresolved resonance region from 4 keV to 100 keV
Bing Jiang(姜炳), Jianlong Han(韩建龙), Jie Ren(任杰), Wei Jiang(蒋伟), Xiaohe Wang(王小鹤), Zian Guo(郭子安), Jianglin Zhang(张江林), Jifeng Hu(胡继峰), Jingen Chen(陈金根), Xiangzhou Cai(蔡翔舟), Hongwei Wang(王宏伟), Longxiang Liu(刘龙祥), Xinxiang Li(李鑫祥), Xinrong Hu(胡新荣), and Yue Zhang(张岳). Chin. Phys. B, 2022, 31(6): 060101.
[11] Neutron activation cross section data library
Xiao-Long Huang(黄小龙), Zhi-Gang Ge(葛智刚), Yong-Li Jin(金永利), Hai-Cheng Wu(吴海成), Xi Tao(陶曦),Ji-Min Wang(王记民), Li-Le Liu(刘丽乐), Yue Zhang(张玥), and Xiao-Fei Wu(吴小飞). Chin. Phys. B, 2022, 31(6): 060102.
[12] Measurements of the 107Ag neutron capture cross sections with pulse height weighting technique at the CSNS Back-n facility
Xin-Xiang Li(李鑫祥), Long-Xiang Liu(刘龙祥), Wei Jiang(蒋伟), Jie Ren(任杰), Hong-Wei Wang(王宏伟), Gong-Tao Fan(范功涛), Jian-Jun He(何建军), Xi-Guang Cao(曹喜光), Long-Long Song(宋龙龙),Yue Zhang(张岳), Xin-Rong Hu(胡新荣), Zi-Rui Hao(郝子锐), Pan Kuang(匡攀), Bing Jiang(姜炳),Xiao-He Wang(王小鹤), Ji-Feng Hu(胡继峰), Jin-Cheng Wang(王金成), De-Xin Wang(王德鑫),Su-Yalatu Zhang(张苏雅拉吐), Ying-Du Liu(刘应都), Xu Ma(麻旭), Chun-Wang Ma(马春旺),Yu-Ting Wang(王玉廷), Zhen-Dong An(安振东), Jun Su(苏俊), Li-Yong Zhang(张立勇),Yu-Xuan Yang(杨宇萱), Wen-Bo Liu(刘文博), Wan-Qing Su(苏琬晴),Sheng Jin(金晟), and Kai-Jie Chen(陈开杰). Chin. Phys. B, 2022, 31(3): 038204.
[13] An ultra-wideband 2-bit coding metasurface using Pancharatnam—Berry phase for radar cross-section reduction
Bao-Qin Lin(林宝勤), Wen-Zhun Huang(黄文准), Lin-Tao Lv(吕林涛), Jian-Xin Guo(郭建新),Yan-Wen Wang(王衍文), and Hong-Jun Ye(叶红军). Chin. Phys. B, 2022, 31(3): 034204.
[14] A novel polarization converter based on the band-stop frequency selective surface
Kun Liao(廖昆), Shining Sun(孙世宁), Xinyuan Zheng(郑昕原), Xianxian Shao(邵纤纤), Xiangkun Kong(孔祥鲲), and Shaobin Liu(刘少斌). Chin. Phys. B, 2022, 31(2): 024211.
[15] Electron excitation processes in low energy collisions of hydrogen-helium atoms
Kun Wang(王堃), Chuan Dong(董川), Yi-Zhi Qu(屈一至), Ling Liu(刘玲), Yong Wu(吴勇),Xu-Hai Hong(洪许海), and Robert J. Buenker. Chin. Phys. B, 2022, 31(12): 123401.
No Suggested Reading articles found!