Abstract
In this paper, A new 3D multi-scroll hidden attractor chaotic system is proposed. The proposed system has chaotic attractors with no equilibrium point, one stable equilibrium point and several stable equilibria. And these three types of hidden attractors can be obtained just through varying a parameter of the system. In the other hand, multi-scroll attractors are generated by a piecewise linear function. The phase diagrams and basins of attraction are respectively used to prove that this system has multi-scroll attractors and hidden attractors. There are also some other powerful tools to analyze the dynamical characteristics of this system like Lyapunov spectrums, bifurcation diagrams and Poincaré maps. This system has great application prospects in communication encryption due to the complex dynamic behaviors of the multi-scroll chaotic attractors and the security of the hidden attractors. Moreover, we accomplish the circuit experiment, and verify the feasibility of each case of the multi-scroll hidden attractor chaotic system.
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All data generated or analyzed during this study are included in this published article.
References
C. Seneviratne, H. Leung, Eur. Phys. J. Spec. Top. 226, 3287 (2017)
F. Yu, S. Qian, X. Chen, Int. J. Bifurc. Chaos 30, 2050147 (2020)
Y. Chu, C. Gao, X. Liu, Chaos 20, 033102 (2010)
G. Zhang, C. Wang, F. Alzahrani, Chaos Solitons Fract. 108, 15 (2018)
U. Parlitz, H. Suetani, S. Luther, Eur. Phys. J. Spec. Top. 222, 553 (2013)
X. Li, F. Liu, X. Liu, Int. J. Model. Identif. Control 29, 153 (2018)
V. Avrutin, E. Mosekilde, Z.T. Zhusubaliyev, Chaos 25, 043114 (2015)
Y. Wang, R. Yang, Z. Bo, IEEE Trans. Ind. Electron. 65, 800 (2017)
S. Wang, C. Wang, C. Xu, Opt. Lasers Eng. 128, 105995 (2020)
J. Deng, M. Zhou, C. Wang et al., Multimedia Tools Appl. 80, 13821 (2021)
G. Cheng, C. Wang, C. Xu, Multimedia Tools Appl. 79, 29243 (2020)
Q. Lai, B. Norouzi, F. Liu, Chaos Solitons Fract. 114, 230 (2018)
J. Sun, M. Peng, F. Liu, C. Tang, Complexity 2020, 8815315 (2020)
C. Xu, J. Sun, C. Wang, Multimedia Tools Appl. 79, 5573 (2020)
J. Zeng, C. Wang, Secur. Commun. Netw. 2021, 6675565 (2021)
W. Xie, C. Wang, H. Lin, Nonlinear Dyn. https://doi.org/10.1007/s11071-021-06476-2 (2021)
C. Wang, L. Xiong, J. Sun, Nonlinear Dyn. 95, 2893 (2019)
H. Lin, C. Wang, W. Yao, Commun. Nonlinear Sci. Numer. Simul. 90, 105390 (2020)
H. Lin, C. Wang, C. Chen et al., IEEE Trans. Circuits Syst. I. https://doi.org/10.1109/TCSI.2021.3081150 (2021)
E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)
H. Dedieu, M.P. Kennedy, M. Hasler, IEEE Trans. Circuits Syst. II Analog Digit. Signal Processing 40, 634 (1993)
O.E. Rössler, Phys. Lett. A 57, 397 (1976)
G. Chen, Controlling Chaos and Bifurcations in Engineering Systems (CRC Press, Boca Raton, 1999)
L.P. Šil’nikov, Dokl. Akad. Nauk SSSR 160, 558 (1965)
X. Wang, G. Chen, Commun. Nonlinear Sci. Numer. Simul. 17, 1264 (2012)
G.A. Leonov, N.V. Kuznetsov, Int. J. Bifurc. Chaos 23, 1330002 (2013)
X. Peng, Y.C. Zeng, Chaos Solitons Fract. 139, 110044 (2020)
X. Wang, Ü. Çavuşoğlu, S. Kacar et al., Appl. Sci. 9, 7812019 (2019)
S. Mobayen, C.K. Volos, Ü. Çavuşoğlu et al., Symmetry 12, 2047 (2020)
S.T. Kingni, G.F. Kuiate, V.K. Tamba et al., J. Comput. Nonlinear Dyn. 14 (2019)
Z. Wang, A. Akgul, V.T. Pham et al., Nonlinear Dyn. 89, 1877 (2017)
M. Molaie, S. Jafari, J.C. Sprott, Int. J. Bifurc. Chaos 23, 699 (2013)
Q. Yang, Z. Wei, G. Chen, Int. J. Bifurc. Chaos 20, 1061 (2010)
H. Bi, G. Qi, J. Hu, Chaos Solitons Fract. 138, 109815 (2020)
L. Zhou, C. Wang, L. Zhou, Int. J. Circuit Theory Appl. 46, 84 (2018)
Q. Tan, Y. Zeng, Z. Li, Nonlinear Dyn. 94, 1585 (2018)
J. Bao, Y. Liu, Adv. Differ. Equ. 2019, 345 (2019)
Q. Xu, Y. Lin, B. Bao et al., Chaos Solitons Fract. 83, 186 (2016)
Y. Li, X. Xia, Y. Zeng et al., Complexity 2020 (2020)
H. Bao, M. Chen, H.G. Wu et al., Sci. China Technol. Sci. 1 (2019)
Q. Lai, Z. Wan, P.D.K. Kuate, H. Fotsin, Commun. Nonlinear Sci. Numer. Simul. 89, 105341 (2020)
Q. Lai, Z. Wan, P.D.K. Kuate, Electron. Lett. 56, 1044 (2020)
F. Yu, L. Liu, H. Shen, Z. Zhang, Y. Huang, S. Cai, Z. Deng, Q. Wan, Mathe. Probl. Eng. 2020, 7530976 (2020)
Q. Lai, S. Chen, Int. J. Bifurc. Chaos 26, 1650177 (2016)
W. Yao, C. Wang, Y. Sun, Appl. Math. Comput. 386, 125483 (2020)
Q. Wan, Z. Zhou, W. Ji, C. Wang, F. Yu, Complexity 2020, 7106861 (2020)
H. Bao, D. Zhu, W. Liu et al., Int. J. Bifurc. Chaos 30, 2050045 (2020)
H. Wu, Y. Ye, M. Chen et al., IEEE Access 7, 145022 (2019)
H. Lin, C. Wang, Y. Tan, Nonlinear Dyn. 99, 2369 (2020)
F. Yu, L. Liu, H. Shen, Z. Zhang, Y. Huang, Complexity 2020, 5904607 (2020)
X. Zhang, C. Wang, W. Yao, Nonlinear Dyn. 97, 2159 (2019)
C. Wang, H. Xia, L. Zhou, Pramana 88, 34 (2017)
Q. Wu, Q. Hong, X. Liu et al., Chaos Solitons Fract. 134, 109727 (2020)
H.G. Wu, Z. Liu, B.C. Bao, Acta Phys. Sin. 60, 090502 (2011)
D. Chang, Z. Li, M. Wang et al., AEU Int. J. Electron. Commun. 88, 20 (2018)
C. Wang, H. Xia, L. Zhou, Int. J. Bifurc. Chaos 27, 1750091 (2017)
Y. Huang, Y. Chen, K. Li, Opt. Commun. 471, 126009 (2020)
F. Wang, B. Zhu, K. Wang et al., IEEE Photon. Technol. Lett. 32, 1303 (2020)
C. Zhao, H. Ren, Nonlinear Dyn. 100, 1 (2020)
Y. Lin, C.H. Wang, H. Xu, Acta Phys. Sin. 61, 240503 (2012)
Y. Li, Z. Li, M. Ma et al., Multimedia Tools Appl. 79, 29161 (2020)
X. Hu, C. Liu, L. Liu, Nonlinear Dyn. 86, 1725 (2016)
Q. Deng, C. Wang, Chaos 29, 093112 (2019)
Q. Deng, C. Wang, L. Yang, Int. J. Bifurc. Chaos 30, 2050086 (2020)
X. Zhang, C. Wang, Int. J. Bifurc. Chaos 29, 1950117 (2019)
Q. Zhao, C. Wang, X. Zhang, Chaos 29, 013141 (2019)
L. Zhou, C. Wang, L. Zhou, Int. J. Circuit Theory Appl. 46, 84 (2018)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (no. 61971185) and Natural Science Foundation of Hunan Province (2020JJ4218).
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Wu, Y., Wang, C. & Deng, Q. A new 3D multi-scroll chaotic system generated with three types of hidden attractors. Eur. Phys. J. Spec. Top. 230, 1863–1871 (2021). https://doi.org/10.1140/epjs/s11734-021-00119-8
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DOI: https://doi.org/10.1140/epjs/s11734-021-00119-8