Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network
Ai-Xue Qi(齐爱学)1, Bin-Da Zhu(朱斌达)2, and Guang-Yi Wang(王光义)2,†
1 Faculty of Aerospace Engineering, Binzhou University, Binzhou 256603, China; 2 Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
Abstract This paper presents a new hyperbolic-type memristor model, whose frequency-dependent pinched hysteresis loops and equivalent circuit are tested by numerical simulations and analog integrated operational amplifier circuits. Based on the hyperbolic-type memristor model, we design a cellular neural network (CNN) with 3-neurons, whose characteristics are analyzed by bifurcations, basins of attraction, complexity analysis, and circuit simulations. We find that the memristive CNN can exhibit some complex dynamic behaviors, including multi-equilibrium points, state-dependent bifurcations, various coexisting chaotic and periodic attractors, and offset of the positions of attractors. By calculating the complexity of the memristor-based CNN system through the spectral entropy (SE) analysis, it can be seen that the complexity curve is consistent with the Lyapunov exponent spectrum, i.e., when the system is in the chaotic state, its SE complexity is higher, while when the system is in the periodic state, its SE complexity is lower. Finally, the realizability and chaotic characteristics of the memristive CNN system are verified by an analog circuit simulation experiment.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61771176 and 62171173).
Corresponding Authors:
Guang-Yi Wang
E-mail: wanggyi@163.com
Cite this article:
Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义) Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network 2022 Chin. Phys. B 31 020502
[1] Chua L 1971 IEEE Trans. Circuit Theory18 507 [2] Strukov D B, Snider G S, Stewart D R and Stanley Williams R 2008 Nature453 80 [3] Chen L, He Z L, Li C D and Umar H G A 2019 Advances in Difference Equations132 [4] Chen L, He, Z, Li C, Wen S and Chen Y 2020 Int. J. Bifur. Chaos30 2050172 [5] Chua L and Yang L 1998 IEEE Trans. Circ. Syst.35 1257 [6] Chua L and Yang L 1998 IEEE Trans. Circ. Syst.35 1273 [7] Vaidyanathan S 2015 International Journal of PharmTech Research8 632 [8] Hu G, Rong J and Kou W 2018 Journal of Digital Information Management16 246 [9] Karakaya B, Celik V and Gulten A 2017 Int. J. Circ. Theory Appl.45 1885 [10] Korn H and Faure P 2003 C. R. Biologies326 787 [11] Chua L and Roska T 2003 Int. J. Bifur. Chaos13 1 [12] Chen A and Yuan S 2001 Journal of Chenzhou Teachers College22 6 [13] Arena P, Baglio S, Fortuna L and Manganaro M 1995 IEEE Trans. Circ. Syst. I:Fundamental Theory and Applications42 123 [14] Chen L, Li C and Chen Y 2018 Int. J. Bifur. Chaos28 1850080 [15] Chen L, Li C D, Huang T W, Hu X F and Chen Y R 2016 Neurocomputing171 1637 [16] Itoh M 2019 Neural and Evolutionary Computing [17] Itoh M and Chua L 2009 Int. J. Bifur. Chaos19 3605 [18] Ahn B H, Lee J, Lin J M, Cheng H P, Hou J L and Esmaeilzadeh H 2020 arXiv:2003. 02369v1[cs. DC] [19] Hu X, Feng G, Duan S and Liu L 2015 Neurocomputing162 150 [20] Li Q, Tang S and Zeng H 2014 Nonlinear Dyn.78 1087 [21] Pham V T and Jafari S 2016 Science China Technological Sciences59 358 [22] Huang X, Zhao Z and Wang Z 2012 Neurocomputing94 13 [23] Hu X F, Wang W H, Sun B, Wang Y C, Li J and Zhou G D 2021 J. Phys. Chem. Lett.12 5377 [24] Liu H J, Chen C L, Zhu X, et al. 2020 Chin. Phys. B29 028502 [25] Xue W H, Ci W J, Xu X H, et al. 2020 Chin. Phys. B29 048401 [26] Shao N, Zhang S B and Shao S Y 2019 Acta Phys. Sin.68 198502 (in Chinese) [27] Bao B C, Qian H and Xu Q 2017 Frontiers in Computational Neuroscience23 00081 [28] Buscarino A and Fortuna L 2011 International Symposium on Signals, IEEE [29] Liao L Y and Zhang X 2017 Journal of Computational and Nonlinear Dynamics12 031002 [30] Yuan F, Wang G Y and Wang X Y 2015 Chin. Phys. B24 060506 [31] Li C B, Sprott J C, Julien and Xing H Y 2016 Int. J. Bifur. Chaos26 1650233 [32] Staniczenko P P A, Lee C F and Jones N S 2009 Phys. Rev. E79 011915
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
