Abstract
In this paper, flux controlled quadratic memductance-based extreme multistable novel 4D hyperchaotic system and its active-adaptive projective synchronisation control is proposed. The proposed memristor-based extreme multistable hyperchaotic system has unstable line of equilibria and coexisting attractors. Different tools such as phase plane, time series, Lyapunov exponents, Lyapunov spectrum, Lyapunov dimension, Poincaré map and recurrence analysis are used to evidence the different dynamic behaviours of the proposed 4D extreme multistable hyperchaotic system. The system shows twisted leaf shaped unique Poincaré behaviour. Bifurcation plot is used to show the extreme multistability and coexisting behaviour in the proposed hyperchaotic system. Further, a nonlinear active-adaptive control is designed for the projective synchronisation between the proposed hyperchaotic and unknown parameter-based extreme multistable hyperchaotic systems. Active-adaptive control laws are designed by using relevant state variables of both known and unknown parameter-based hyperchaotic systems and required adaptive estimation laws are designed for error convergence. The required global asymptotic stability is ensured via Lyapunov’s theorem of stability. Simulation is presented in MATLAB environment to demonstrate the effective verification of the theoretical approach and the objectives are attained successfully. Finally, the hardware implementation of proposed hyperchaotic system is accomplished using NI-MyRIO 1900 processor.
Similar content being viewed by others
Data Availability Statement
All data generated or analysed data during this study are included in the manuscript.
References
G. Chen, X. Dong, From chaos to order: methodologies, perspectives and applications (World Scientific, Singapore, 1998), pp. 311–387
P.P. Singh, K.M. Singh, B.K. Roy, Eur. Phys. J. Special Topics 227, 731–746 (2018)
P.P. Singh, B.K. Roy, Annual Reviews in Control 45, 152–165 (2018)
Q. Lai, Z. Wan, H. Zhang, G. Chen, IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3146570
Q. Lai, H. Zhang, P.D.K. Kuate, G. Xu, X.-W. Zhao, Appl. Intell. (2022). https://doi.org/10.1007/s10489-021-03071-1
P.P. Singh, J.P. Singh, B.K. Roy, IETE J. Research 63, 853–869 (2017)
J.P. Singh, B.K. Roy, Trans. Inst. Meas. Control 40, 3573–3586 (2017)
P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Application 9, 171–183 (2016)
P.P. Singh, B.K. Roy, C. Volos, (2021) Mem-elements for Neuromorphic Circuits with Artificial Intelligence Applications. In: Volos and Pham eds. Elsevier Academic Press: United Kingdom. 9: 183-205.
P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Application 8, 995–1004 (2015)
Q. Lai, B. Norouzi, F. Liu, Chaos, Solitons. Fractals 114, 230–245 (2020)
P.P. Singh, J.P. Singh, B.K. Roy, Chaos. Solitons and Fractals 69, 31–39 (2014)
J.P. Singh, B.K. Roy, S. Jafari, Chaos, Solitons. Fractals 106, 243–257 (2018)
J.P. Singh, B.K. Roy, Optik-Int. J. Light and Electron Optics 145, 209–217 (2017)
J.P. Singh, B.K. Roy, Int. J. Dyn. Control 45, 1–10 (2017)
P.P. Singh, J.P. Singh, M. Borah, B.K. Roy, IFAC-PapersOnLine 49, 522–525 (2016)
S. Jafari, V.T. Pham, T. Kapitaniak, Int. J. Bifurcation Chaos 26, 1650031–1650036 (2016)
S. Jafari, J.C. Sprott, F. Nazarimehr, Eur. Phys. J. Special Topics 224, 1469–1476 (2015)
Q. Lai, Z. Wan, P.D.K. Kuate, Elect. Lett. 56, 1044–1046 (2020)
Z. Wei, I. Moroz, J.C. Sprott, A. Akgul, W. Zhang, Chaos 27, 033101–033108 (2017)
Q. Lai, Z. Wan, L.K. Kengne, P.D.K. Kuate, C. Chen, IEEE Trans. Circuits Syst. II: Express Briefs 68, 2197–2201 (2021)
Z. Wei, W. Zhang, Z. Wang, M. Yao, Int. J. Bifurcation Chaos 25, 1550028–1550036 (2015)
Leon O. Chua, IEEE Trans. Circuit Theory 18, 507–519 (1971)
D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)
L. Wang, T. Dong, M.F. Ge, Applied Mathematics and Computation 347, 293–305 (2019)
K. Usha, P.A. Subha, Bio Systems 178, 1–9 (2019)
Y. Cao, Y. Cao, S. Wen, T. Huang, Z. Zeng, Neural Networks 109, 159–167 (2019)
Q. Lai, C. Lai, P.D.K. Kuate, C. Li, S. He, Int. J. Bifurcation Chaos 32, 2250042 (2022)
Z. Li, C. Zhou, M. Wang, Int. J. Electron. Commun. (AEU) 100, 127–137 (2019)
V. Sundarapandian, A. Sambas, M. Mamat, M. Sanjaya, Arch. Contr. Sci. 100, 541–554 (2017)
M. Itoh, Leon O. Chua, Int. J. Bifurcation Chaos 18, 3183–3206 (2008)
B. Muthuswamy, IETE Tech. Rev. 26, 1–16 (2009)
Y. Zhong Qi-Shui, Y-B, Y Jue-Bang. Chinese Phys., Lett. 27: 8250. (2010)
B. Muthuswamy, Leon O. Chua. Int. J. Bifurcation Chaos 20, 1567–1580 (2010)
D. Batas, H. Fiedler, IEEE Trans. Nanotechnol. 10, 250–255 (2011)
H. Kim, MPd. Sah, C. Yang, S. Cho, Leon O. Chua, IEEE Trans. Circ. Syst. I: Regular Papers. 59, 2422–2431 (2012)
Y. Li, X. Huang, M. Guo, Math. Probl. Eng. 2013, 398306 (2013)
H. Li, L. Wang, S. Duan, Int. J. Bifurcation Chaos (2014). https://doi.org/10.1142/S0218127414500990
S.C. Yener, H.H. Kuntman, Radio Eng. 23, 1140–1149 (2014)
X. Hu, S. Duan, J. Eng. Sci. Technol. Rev. 8, 17–23 (2015)
Z. Chen, H. Tang, Z. Wang, Q. Zhang, J. Han, J. Appl. Anal. Comput. 5, 251–261 (2015). https://doi.org/10.11948/2015023
J. Ma, Z. Chen, Z. Wang, Q. Zhang, Nonlinear Dyn. 81, 1275–1288 (2015)
Xu. Ya-Ming, Li-Dan. Wang, Shu-Kai. Duan, Acta Phys. Sini. 65, 120503 (2016). https://doi.org/10.7498/aps.65.120503
A.H. Abolmasoumi, S. Khosravinejad, Int. J. Comput. Theory Eng. 8, 506–511 (2016)
F. Yuan, G. Wang, X. Wang, Chaos 26, 073107 (2016). https://doi.org/10.1063/1.4958296
W. Xiong, J. Huang, Adv. Differen. Equat. 26, 1–9 (2016). https://doi.org/10.1186/s13662-016-0789-3
Q. Hu, Y. Yu, F. Lie, H. Zhang, Youth Acad. Annual Conf. Chin. Associat. Automat 31 (Wuhan, China, 2016), pp. 11–13
C. Wang, H. Xia, L. Zhou, Pramana-J. Phys. 88, 34–45 (2017). https://doi.org/10.1007/s12043-016-1342-3
S.C. Yener, C. Barbaros, R. Mutlu, E. Karakulak, Acta Phys. Polonica A 132, 134–145 (2017). https://doi.org/10.12693/APhysPolA.132.1058
K. Rajagopal, L. Guessas, A. Karthikeyan, A. Srinivasan, G. Adam, Complexity (2017). https://doi.org/10.1155/2017/1892618
P. Prakash, J.P. Singh, B.K. Roy, IFAC PapersOnLine 51, 1–6 (2018)
K. Ding, Complexity (2017). https://doi.org/10.1155/2018/5431619
K. Rajagopal, H. Jahanshahi, M. Varan, I. Bayir, V.T. Pham, S. Jafari, A. Karthikeyan, Int. J. Electron. Commun. (AEU) 94, 55–68 (2018)
K. Rajagopal, S. Arun, A. Karthikeyan, P. Duraisamy, A. Srinivasan, Int. J. Electron. Commun. (AEU) 95, 249–255 (2018)
B. Wang, F.C. Zou, J. Cheng, Optik 154, 538–544 (2018)
B. Wang, F.C. Zou, Y. Zhang, Optik 172, 873–878 (2018)
X. Wang, M. Gao, X. Min, Z. Lin, H. Ho-ChingIu, IEEE Access. 8, 182240–48 (2020)
P.D.K. Kuate, Q. Lai, H. Fotsin, Eur. Phys. J. Special Topics 228, 2171–2184 (2019)
K. Rajagopal, S. Jafari, A. Karthikeyan, A. Srinivasan, B. Ayele, Circuits Syst Signal Process 37, 3702–3724 (2018)
F. Yu, S. Qian, Xi Chen, Y. Huang, Li Liu, C. Shi, S. Cai, Y. Song. (2020). Int. J. Bifurcation Chaos. 30: 2050147-2050172
F. Yu, L. Liu, S. Qian, L. Li, Y. Huang, C. Shi, S. Cai, X. Wu, S. Du, Q. Wan, Complexity. (2020). https://doi.org/10.1155/2020/8034196
F. Yu, S. Qian, Xi Chen, Y. Huang, S. Cai, J. Jin, S. Du. Complexity.(2021). 10.1155/2021/6683284
N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Physics Reports 438, 237–329 (2020)
H. Kantz, T. Schreiber, Nonlinear Time Series Analysis (University Press, Cambridge, 1997)
J. E. Slotine, W. Li, Applied nonlinear control, Prentice Hall Inc., Englewood Cliffs, New Jersey (1991) 100-154, 276-311
Author information
Authors and Affiliations
Contributions
P. P. Singh originated the idea, performed the analysis, numerical computations and wrote the draft, and A. Rai participated in physical realisation presented in the manuscript. B. K. Roy guided in the concept, corrected the primary and revised manuscript.
Corresponding author
Ethics declarations
Conflict of interest
Authors do not have any financial and non-financial interests to declare. The authors did not receive support from any organisation for the submitted work.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Singh, P.P., Rai, A. & Roy, B.K. Memristor-based asymmetric extreme multistable hyperchaotic system with a line of equilibria, coexisting attractors, its implementation and nonlinear active-adaptive projective synchronisation. Eur. Phys. J. Plus 137, 875 (2022). https://doi.org/10.1140/epjp/s13360-022-03063-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-022-03063-1