Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors
Li-Lian Huang(黄丽莲)1,2, Shuai Liu(刘帅)1,2, Jian-Hong Xiang(项建弘)1,2,†, and Lin-Yu Wang(王霖郁)1,2
1 College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China; 2 MIIT Key Laboratory of Advanced Marine Communication and Information Technology, Harbin 150001, China
Abstract A five-value memristor model is proposed, it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current. Then, based on the classical Liu-Chen system, a new memristor-based four-dimensional (4D) chaotic system is designed by using the five-value memristor. The trajectory phase diagram, Poincare mapping, bifurcation diagram, and Lyapunov exponent spectrum are drawn by numerical simulation. It is found that, in addition to the general chaos characteristics, the system has some special phenomena, such as hidden homogenous multistabilities, hidden heterogeneous multistabilities, and hidden super-multistabilities. Finally, according to the dimensionless equation of the system, the circuit model of the system is built and simulated. The results are consistent with the numerical simulation results, which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61203004), the Natural Science Foundation of Heilongjiang Province, China (Grant No. F201220), and the Heilongjiang Provincial Natural Science Foundation of Joint Guidance Project (Grant No. LH2020F022).
Li-Lian Huang(黄丽莲), Shuai Liu(刘帅), Jian-Hong Xiang(项建弘), and Lin-Yu Wang(王霖郁) Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors 2021 Chin. Phys. B 30 100506
[1] Chua L O 1971 IEEE Trans. Circ. Theory18 507 [2] Chua L O and Kang S M 1976 Proc. IEEE64 209 [3] Strukov D B, Snider G S, Stewart D R and Williams R S 2008 Nature453 80 [4] Itoh M and Chua L O 2008 Int. J. Bifurc. Chaos18 3183 [5] Bao B C, Xu J P and Liu Z 2010 Chin. Phys. Lett.27 070504 [6] Bao B C, Xu J P, Zhou G H, Ma Z H and Zou L 2011 Chin. Phys. B20 120502 [7] Bao B C, Liu Z and Xu J P 2010 Chin. Phys. B19 030510 [8] Muthuswamy B 2010 Int. J. Bifurc. Chaos20 1335 [9] Liu G Z, Zheng L J, Wang G Y, Shen Y R and Liang Y 2019 IEEE Access7 43691 [10] Chen C J, Chen J Q, Bao H, Chen M and Bao B C 2019 Nonlinear Dyn.95 3385 [11] Ying J J, Wang G Y, Dong Y J and Yu S M 2019 Int. J. Bifurc. Chaos29 1930030 [12] Chen J J, Yan D W, Duan S K and Wang L D 2020 Chin. Phys. B29 110504 [13] Muthuswamy B and Kokate P P 2009 IETE Tech. Rev.26 417 [14] Xi H L, Li Y X and Huang X 2014 Entropy16 6240 [15] Bao B C, Jiang T, Xu Q, Chen M, Wu H G and Hu Y H 2016 Nonlinear Dyn.86 1711 [16] Wang G Y, Yuan F, Chen G R 2018 Chaos28 013125 [17] Zhou W, Wang G Y, Shen Y R 2018 Int. J. Bifurc. Chaos28 1830033 [18] Zhang X, Wang C H. 2019 Int. J. Bifurc. Chaos29 1950117 [19] Deng Q L, Wang C H and Yang L M 2020 Int. J. Bifurc. Chaos30 2050086 [20] Yan B, He S B and Wang S J 2020 Math. Probl. Eng.2020 2468134 [21] Gu S Q, He S B, Wang H H and Du B X 2021 Chaos, Solitons, and Fractals143 110613 [22] Wang X Y, Zhang X and Gao M 2020 Complexity2020 6949703 [23] Huang L L, Yao W J, Xiang J H and Zhang Z F 2020 Complexity2020 2408460 [24] Chua L O 2011 Appl. Phys. A102 765 [25] Chua L O 2012 Proc. IEEE100 1920 [26] Adhikari S P, Sah M P, Kim H and Chua L O 2013 IEEE Trans. Circ. Syst. I: Reg. Papers60 3008 [27] Liu W B and Chen G R 2003 Int. J. Bifurc. Chaos13 261 [28] Liu W B and Chen G R 2004 Int. J. Bifurc. Chaos14 1395 [29] Khan A and Singh S 2018 Chin. J. Phys.56 238 [30] Gottwald G A and Melbourne I 2004 Proc. Math. Phys. Eng. Sci.460 603
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