A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

doi:10.1088/1674-1056/27/10/100501

中国物理B ›› 2018, Vol. 27 ›› Issue (10): 100501-100501.doi: 10.1088/1674-1056/27/10/100501

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

J P Singh, V T Pham, T Hayat, S Jafari, F E Alsaadi, B K Roy

1 Department of Electrical Engineering, National Institute of Technology Silchar, 788010, India;
2 School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
4 Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;
5 Ambikar University of Technology, Tehran, 15875-4413, Iran;
6 Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia

收稿日期:2018-04-07 修回日期:2018-07-20 出版日期:2018-10-05 发布日期:2018-10-05
通讯作者: J P Singh E-mail:jayprakash1261@gmail.com

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

J P Singh¹, V T Pham², T Hayat^3,4, S Jafari⁵, F E Alsaadi⁶, B K Roy¹

1 Department of Electrical Engineering, National Institute of Technology Silchar, 788010, India;
2 School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
4 Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;
5 Ambikar University of Technology, Tehran, 15875-4413, Iran;
6 Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia

Received:2018-04-07 Revised:2018-07-20 Online:2018-10-05 Published:2018-10-05
Contact: J P Singh E-mail:jayprakash1261@gmail.com

摘要/Abstract

摘要：

This paper reports a new simple four-dimensional (4D) hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.

关键词: new hyperjerk chaotic system, stable equilibrium, hidden attractors, adaptive backstepping control, synchronization

Abstract:

Key words: new hyperjerk chaotic system, stable equilibrium, hidden attractors, adaptive backstepping control, synchronization

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Gg (Control of chaos, applications of chaos) 05.45.Jn (High-dimensional chaos)

J P Singh, V T Pham, T Hayat, S Jafari, F E Alsaadi, B K Roy. A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control[J]. 中国物理B, 2018, 27(10): 100501-100501.

参考文献 82

[1]	Wang Z, Akgul A, Pham V T and Jafari S 2017 Nonlinear Dyn. 89 1877 doi: 10.1007/s11071-017-3558-2
[2]	Aram Z, Jafari S, Ma J, Sprott J C, Zendehrouh S and Pham V T 2017 Commun. Nonlinear Sci. Numer. Simul. 44 449 doi: 10.1016/j.cnsns.2016.08.025
[3]	Rajagopal K, Karthikeyan A and Srinivasan A K 2017 Nonlinear Dyn. 87 2281 doi: 10.1007/s11071-016-3189-z
[4]	Pham V T, Volos C, Jafari S, Vaidyanathan S, Kapitaniak T and Wang X 2016 Int. J. Bifur. Chaos 26 1650139 doi: 10.1142/S021812741650139X
[5]	Pham V T, Vaidyanathan S, Volos C and Jafari S 2015 Eur. Phys. J. Special Topics 224 1507 doi: 10.1140/epjst/e2015-02476-9
[6]	Shahzad M, Pham V T, Ahmad M, Jafari S and Hadaeghi F 2015 Eur. Phys. J. Special Topics 224 1637 doi: 10.1140/epjst/e2015-02485-8
[7]	Sprott J C 2010 Elegant Chaos:Algebraically Simple Chaotic Flows Singapore:World Scientific
[8]	Chlouverakis K E and Sprott, J 2006 Chaos, Solitons and Fractals 28 739 doi: 10.1016/j.chaos.2005.08.019
[9]	Dalkiran F Y and Sprott J C 2016 Int. J. Bifur. Chaos 26 1650189 doi: 10.1142/S0218127416501893
[10]	Li C, Sprott J C and Xing H 2016 Phys. Lett. A 380 1172 doi: 10.1016/j.physleta.2016.01.045
[11]	Li P, Zheng T, Li C, Wang X and Hu W 2016 Nonlinear Dyn. 86 197 doi: 10.1007/s11071-016-2882-2
[12]	Kengne J, Jafari S, Njitacke Z, Khanian M Y and Cheukem A 2017 Commun. Nonlinear Sci. Numer. Simul. 52 62 doi: 10.1016/j.cnsns.2017.04.017
[13]	Singh P P, Singh J P and Roy B 2014 Chaos, Solitons and Fractals 69 31 doi: 10.1016/j.chaos.2014.09.005
[14]	Singh J P and Roy B 2016 Chaos, Solitons and Fractals 92 73 doi: 10.1016/j.chaos.2016.09.010
[15]	Singh J P and Roy B 2016 Optik 127 11982 doi: 10.1016/j.ijleo.2016.09.107
[16]	Leonov G A, Kuznetsov N V and Mokaev TN H 2015 Eur. Phys. J. Special Topics 224 1421 doi: 10.1140/epjst/e2015-02470-3
[17]	Sharma P, Shrimali M, Prasad A, Kuznetsov N and Leonov G 2015 Eur. Phys. J. Special Topics 224 1485 doi: 10.1140/epjst/e2015-02474-y
[18]	Sharma P R, Shrimali M D, Prasad A, Kuznetsov N and Leonov G 2015 Int. J. Bifur. Chaos 25 1550061 doi: 10.1142/S0218127415500613
[19]	Danca M F and Kuznetsov N 2017 Chaos, Solitons and Fractals 103 144 doi: 10.1016/j.chaos.2017.06.002
[20]	Danca M F, Kuznetsov N and Chen G 2017 Nonlinear Dyn. 88 791 doi: 10.1007/s11071-016-3276-1
[21]	Kuznetsov N, Leonov G, Yuldashev M and Yuldashev R 2017 Commun. Nonlinear Sci. Numer. Simul. 51 39 doi: 10.1016/j.cnsns.2017.03.010
[22]	Leonov G A and Kuznetsov N V 2013 Int. J. Bifur. Chaos 23 1330002 doi: 10.1142/S0218127413300024
[23]	Leonov G, Kuznetsov N, Kiseleva M, Solovyeva E and Zaretskiy A 2014 Nonlinear Dyn. 77 277 doi: 10.1007/s11071-014-1292-6
[24]	Leonov G, Kuznetsov N and Mokaev T 2015 Commun. Nonlinear Sci. Numer. Simul. 28 166 doi: 10.1016/j.cnsns.2015.04.007
[25]	Dudkowski D, Jafari S, Kapitaniak T, Kuznetsov N V, Leonov G A and Prasad A 2016 Phys. Rep. 637 1 doi: 10.1016/j.physrep.2016.05.002
[26]	Molaie M, Jafari S and Sprott J C 2013 Int. J. Bifur. Chaos 23 1350188 doi: 10.1142/S0218127413501885
[27]	Kingni S T, Jafari S, Simo H and Woafo P 2014 Eur. Phys. J. Plus 29 1
[28]	Pham V T, Jafari S, Kapitaniak T, Volos C and Kingni S T 2017 Int. J. Bifur. Chaos 27 1750053 doi: 10.1142/S0218127417500535
[29]	Pham V T, Wang X, Jafari S, Volos C and Kapitaniak T 2017 Int. J. Bifur. Chaos 27 1750097 doi: 10.1142/S0218127417500973
[30]	Brezetskyi S, Dudkowski D and Kapitaniak T 2015 Eur. Phys. J. Special Topics 224 1459 doi: 10.1140/epjst/e2015-02471-2
[31]	Singh J P and Roy B 2017 Int. J. Dyn. Control 6 529
[32]	Wei Z 2011 Phys. Lett. A 376 102 doi: 10.1016/j.physleta.2011.10.040
[33]	Pham V T, Kingni S T, Volos C, Jafari S and Kapitaniak T 2017 AEU-Int. J. Electron. Commun. 78 220 doi: 10.1016/j.aeue.2017.04.012
[34]	Pham V T, Volos C, Jafari S and Kapitaniak T 2017 Nonlinear Dyn. 87 2001 doi: 10.1007/s11071-016-3170-x
[35]	Singh J P and Roy B 2017 Optik 145 209 doi: 10.1016/j.ijleo.2017.07.042
[36]	Singh J P and Roy B 2017 Nonlinear Dyn. 89 1845 doi: 10.1007/s11071-017-3556-4
[37]	Barati K, Jafari S, Sprott J C and Pham V T 2016 Int. J. Bifur. Chaos 26 1630034 doi: 10.1142/S0218127416300342
[38]	Pham V T, Jafari S and Volos C 2017 Optik 131 343 doi: 10.1016/j.ijleo.2016.11.064
[39]	Tlelo-Cuautle E, de la Fraga L G, Pham V T, Volos C, Jafari S and de Jesus Quintas-Valles A 2017 Nonlinear Dyn. 89 1 doi: 10.1007/s11071-017-3432-2
[40]	Elhadj Z and Sprott J 2013 Palestine J. Math. 2 38
[41]	Wang X, Vaidyanathan S, Volos C, Pham V T and Kapitaniak T 2017 Nonlinear Dyn. 89 1 doi: 10.1007/s11071-017-3432-2
[42]	Daltzis P, Vaidyanathan S, Pham V T, Volos C, Nistazakis E and Tombras G 2017 Circ. Sys. Signal Process. 1
[43]	Lai Q and Chen S 2016 Int. J. Control. Autom. Syst. 14 1124 doi: 10.1007/s12555-015-0056-5
[44]	Qiang L, Tsafack N, Jacques K and Zhao X W 2018 Chaos, Solitons and Fractals 107 92 doi: 10.1016/j.chaos.2017.12.023
[45]	Lai Q, Akgul A, Zhao X W and Pei H 2017 Int. J. Bifurc. Chaos 27 1750142 doi: 10.1142/S0218127417501425
[46]	Lai Q, Akgul A, Li C, Xu G and Çavuşoǧlu Ü 2018 Entropy 20 1
[47]	Ling G, Guan Z, Hu B, Lai Q and Wu Y 2017 IEEE Trans. Nanobiosci. 16 216 doi: 10.1109/TNB.2017.2669112
[48]	Guan Z H, Lai Q, Chi M, Cheng X M and Liu F 2014 Nonlinear Dyn. 75 331 doi: 10.1007/s11071-013-1069-3
[49]	Li C, Sprott J C, Kapitaniak T and Lu T 2018 Chaos, Solitons and Fractals 109 76 doi: 10.1016/j.chaos.2018.02.022
[50]	Li C, Thio W J, Iu H H and Lu T 2018 IEEE Access 6 12945 doi: 10.1109/ACCESS.2017.2788408
[51]	Li C, Thio W J, Sprott J C, Herbert H C and Xu Y 2018 IEEE Access 6 1 doi: 10.1109/ACCESS.2018.2812929
[52]	Kingni S, Jafari S, Simo H and Woafo P 2014 Eur. Phys. J. Plus 129 76 doi: 10.1140/epjp/i2014-14076-4
[53]	Zhusubaliyev Z T, Mosekilde E, Rubanov V G and Nabokov R A 2015 Physica D:Nonlinear Phenomena 30 6
[54]	Wei Z, Moroz I, Wang Z, Sprott J C and Kapitaniak T 2016 Int. J. Bifur. Chaos 26 1650125 doi: 10.1142/S021812741650125X
[55]	Wang X, Pham V T, Jafari S, Volos C, Munoz-Pacheco J M and Tlelo-Cuautle E 2017 IEEE Access 5 8851 doi: 10.1109/ACCESS.2017.2693301
[56]	Wei Z and Wang Z 2013 Kybernetika 49 359
[57]	Wei Z and Yang Q 2011 Nonlinear Analysis:Real World Applications 12 106 doi: 10.1016/j.nonrwa.2010.05.038
[58]	Wei Z, Zhang W, Wang Z and Yao M 2015 Int. J. Bifur. Chaos 25 1550028 doi: 10.1142/S0218127415500285
[59]	Wei Z and Pehlivan I 2012 Optoelectronics and Advanced Materials-Rapid Communications 6 742
[60]	Wei Z 2012 Computers and Mathematics with Applications 63 728 doi: 10.1016/j.camwa.2011.11.037
[61]	Wei Z and Yang Q 2012 Nonlinear Dyn. 68 543 doi: 10.1007/s11071-011-0235-8
[62]	Wang X and Chen G 2012 Commun. Nonlinear Sci. Numer. Simul. 17 1264 doi: 10.1016/j.cnsns.2011.07.017
[63]	Wei Z and Zhang W 2014 Int. J. Bifur. Chaos 24 1450127 doi: 10.1142/S0218127414501272
[64]	Wei Z, Yu P, Zhang W and Yao M 2015 Nonlinear Dyn. 82 131 doi: 10.1007/s11071-015-2144-8
[65]	Lai Q and Chen S 2016 Int. J. Bifur. Chaos 26 1650177 doi: 10.1142/S0218127416501777
[66]	Kapitaniak T and Leonov G A 2015 Eur. Phys. J. Special Topics 224 1405 doi: 10.1140/epjst/e2015-02468-9
[67]	Maistrenko Y, Kapitaniak T and Szuminski P 1997 Phys. Rev. E 56 6393 doi: 10.1103/PhysRevE.56.6393
[68]	Blażejczyk-Okolewska B and Kapitaniak T 1998 Chaos, Solitons and Fractals 9 1439 doi: 10.1016/S0960-0779(98)00164-7
[69]	Silchenko A, Kapitaniak T and Anishchenko V 1999 Phys. Rev. E 59 1593 doi: 10.1103/PhysRevE.59.1593
[70]	Wang Z, Yuan J and Wei J 2017 Optik 137 85 doi: 10.1016/j.ijleo.2017.02.070
[71]	Singh P P, Singh J P and Roy B K 2017 IETE J. Res. 69 853
[72]	Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821 doi: 10.1103/PhysRevLett.64.821
[73]	Miao Q, Tang Y, Lu S and Fang J 2009 Nonlinear Dyn. 57 107 doi: 10.1007/s11071-008-9424-5
[74]	Khan M A and Poria S 2013 Pramana. 81 395 doi: 10.1007/s12043-013-0592-6
[75]	Singh J P and Roy B K 2017 , DOI: 0142331217727580 doi: 0142331217727580
[76]	Chen M, Wu Q and Jiang C 2012 Nonlinear Dyn. 70 2421 doi: 10.1007/s11071-012-0630-9
[77]	Hu C and Yu J 2016 Chaos, Solitons and Fractals 91 262 doi: 10.1016/j.chaos.2016.06.004
[78]	Khalil H K 1996 (New Jersey:Prentice-Hall) 2
[79]	Jafari M A, Mliki E, Akgul A, et al. 2017 Nonlinear Dyn. 88 2303 doi: 10.1007/s11071-017-3378-4
[80]	Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Physica D:Nonlinear Phenomena 16 285 doi: 10.1016/0167-2789(85)90011-9
[81]	Ma J, Wu X, Chu R and Zhang L 2014 Nonlinear Dyn. 76 1951 doi: 10.1007/s11071-014-1260-1
[82]	Li Q, Zeng H and Li J 2015 Nonlinear Dyn. 79 2295 doi: 10.1007/s11071-014-1812-4

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

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