|
|
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.
|
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)
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|