Abstract
In this paper, two kinds of novel non-ideal voltage-controlled multi-piecewise cubic nonlinearity memristors and their mathematical models are presented. By adding the memristor to the circuit of a three-dimensional jerk system, a novel memristive multiscroll hyperchaotic jerk system is established without introducing any other ordinary nonlinear functions, from which \(2N+2\)-scroll and \(2M+1\)-scroll hyperchaotic attractors are achieved. It is exciting to note that this new memristive system can produce the extreme multistability phenomenon of coexisting infinitely multiple attractors. Furthermore, the dynamical behaviours of the proposed system are analysed by phase portraits, equilibrium points, Lyapunov exponents and bifurcation diagrams. The results indicate that the system exhibits hyperchaotic, chaotic and periodic dynamics. Especially, the phenomenon of transient chaos can also be found in this memristive multiscroll system. Additionally, the MULTISIM circuit simulations and the hardware experimental results are performed to verify numerical simulations.
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References
L O Chua, IEEE Trans. Circuit Theory 18, 507 (1971)
D B Strukov, G S Snider, D R Stewart and R S Williams, Nature 453, 80 (2008)
M Itoh and L O Chua, Int. J. Bifurc. Chaos 18(11), 3183 (2008)
B Muthuswamy and L O Chua, Int. J. Bifurc. Chaos 20, 1567 (2010)
B Muthuswamy and P P Kokate, IETE Tech. Rev. 26(6), 417 (2014)
B C Bao, J P Xu and G H Zhou, Chin. Phys. B 20(12), 113 (2011)
B C Bao, W Hu, J P Xu, Z Liu and L Zou, Acta Phys. Sin. 262, 1775 (2011)
B C Bao, F W Hu and Z Liu, Chin. Phys. B 23(07), 307 (2014)
B C Bao, H Bao, N Wang, M Chen and Q Xu, Chaos Solitons Fractals 94, 102 (2017)
J Ma, Z Q Chen and Z L Wang, Nonlinear Dyn 81, 1275 (2015)
Q Yu, B C Bao, F Hu, Q Xu and M Chen, Acta Phys. Sin. 63, 240505 (2014)
Z J Li and Y C Zeng, Chin. Phys. B 22, 148 (2011)
Q Xu, Y Lin and B C Bao, Chaos Solitons Fractals 83, 186 (2016)
B R Xu, Acta Phys. Sin. 62, 190506 (2013)
H F Li, L D Wang and S K Duan, Int. J. Bifurc. Chaos 24, 1450099 (2014)
C H Wang, H Xia and L Zhou, Int. J. Bifurc. Chaos 27(6), 1750091 (2017)
C H Wang, H Xia and L Zhou, Pramana – J. Phys. 88(2): 34 (2017)
X Y Hu, C X Liu, L Liu, Y P Yao and G C Zheng, Chin. Phys. B 26(11), 110502 (2017)
F Yuan, J Y Wang and X W Wang, Chaos 26, 073107 (2016)
C H Wang, X M Liu and H Xia, Chaos 27(3), 033144 (2017)
U Feudel, Int. J. Bifurc. Chaos 18, 1607 (2008)
C Li and J C Sprott, Int. J. Bifurc. Chaos 24(10), (2014)
A N Pisarchik and U Feudel, Phys. Rep. 540(4), (2014)
S Zhang, Y C Zeng and Z J Li, Chaos 28, 013113 (2018)
C Hens, S K Dana and U Feudel, Chaos 25(5), (2015)
L O Chua, Appl. Phys. A 102, 765 (2011)
S P Adhikari, M P Sah, H Kim and L O Chua, IEEE Trans. Circuits Syst. I: Regul. Pap. 60(11), 3008 (2013)
Z Yan and P Yu, Chaos Solitons Fractals 35, 333 (2008)
C X Liu and J J Lu, Int. J. Bifurc. Chaos 24, 1299 (2010)
F Yuan, G Y Wang and X W Wang, Chaos 26, 073107 (2016)
G B Astaf’ev, A A Koronovskii and A E Hramov, Tech. Phys. Lett. 29, 923 (2003)
S J Cang, G Y Qi and Z Q Chen, Nonlinear Dyn. 59(3), 515 (2010)
Acknowledgements
The work was supported by the National Natural Science Foundations of China under Grant No. 61471310 and the Natural Science Foundations of Hunan Province, China under Grant No. 2015JJ2142.
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Xia, X., Zeng, Y. & Li, Z. Coexisting multiscroll hyperchaotic attractors generated from a novel memristive jerk system. Pramana - J Phys 91, 82 (2018). https://doi.org/10.1007/s12043-018-1657-3
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DOI: https://doi.org/10.1007/s12043-018-1657-3