AccScience Publishing / NSCE / Volume 2 / Issue 1 / DOI: 10.36922/NSCE026050003
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RESEARCH ARTICLE

Dynamics and circuit implementation of a memristive chaotic system with switchable equilibrium and multi-parameter amplitude modulation

Ling Wan 1*
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1 Department of Industrial Automation, Tianyou College, East China Jiaotong University, Nanchang, Jiangxi, China
NSCE 2026, 2(1), 026050003 https://doi.org/10.36922/NSCE026050003
Received: 28 January 2026 | Revised: 2 April 2026 | Accepted: 8 April 2026 | Published online: 8 May 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

The design and implementation of memristive chaotic systems with switchable equilibria and rich dynamic behaviors have become an important research direction in nonlinear science, owing to their unique potential in engineering applications. In this paper, a non-ideal absolute-value memristor is embedded into a three-dimensional chaotic system (NE2), constructing a memristive chaotic system (MCS) with multiple types of equilibrium points. By changing the system parameters, the switching between the states with and without equilibrium points can be achieved. This paper analyzes the dynamic characteristics of MCS using bifurcation diagrams, Lyapunov exponents, and phase projections. It discovers that MCS has multi-parameter amplitude modulation and partial mirror symmetry. Meanwhile, under different parameter settings, MCS can generate a wide variety of chaotic and periodic attractors. The reliability of the theoretical analysis is verified through corresponding circuit experiments, and the oscilloscope measurements are highly consistent with the theoretical conclusions, confirming the validity of the constructed chaotic system and laying the foundation for its practical application.

Keywords
Memristive chaotic system
Switchable equilibrium points
Dynamic characteristics
Circuit implementation
Funding
None.
Conflict of interest
The author declares no conflicts of interest.
References
  1. Lai, Q, Zhu, CK, Zhao, XW, Sun, X, Hua, JL, & Hua, JL. A unified framework for generating 4D discrete memristive hyperchaotic maps with complex dynamics and application to encryption. IEEE Internet of Things J. 2025;12(19):40934-40943. https://doi.org/10.1109/jiot.2025.3590465
  2. Wang, L, Song, W, Di, J, Zhang, X, Zou, C. Image Encryption Method Based on Three-Dimensional Chaotic Systems and V-Shaped Scrambling. Entropy. 2025;27(1):84. https://doi.org/10.3390/e27010084
  3. Zhao, Z, Yang, R, Liu, J, Liu, G. Study on weak signal amplitude detection and circuit simulation based on a new chaotic system. Chaos, Solitons & Fractals. 2025;198:116554. https://doi.org/10.1016/j.chaos.2025.116554
  4. Pan, G, Li, C, Liu, W, Xue, Y, Qi, X. Countless coexisting chaotic attractors: From system construction to FPGA-based observation. Chaos, Sol & Frac. 2025;198:116610. https://doi.org/10.1016/j.chaos.2025.116610
  5. Jie, J, Yang, Y, Zhang, P. The construction method of chaotic system model based on state variables and uncertain variables and its application in image encryption. Appl Math Model. 2025;144:116097. https://doi.org/10.1016/j.apm.2025.116097
  6. Erkan, U, Toktas, A, Toktas, F, Lin, YT, Gao, S. Hybridization of benchmark functions for a high-performance 1D chaotic map and image encryption application. Non lSci and Cont Eng. 2025;1(2):025340010. https://doi.org/10.36922/NSCE025340010
  7. Yang, H, Liu, Y, Li, G. Analysis of 3D chaotic system with novel double scroll structure and additional nonlinear functions and its application in weak signal detection. Eur Phys J Plus. 2025;140(7):637. https://doi.org/10.1140/epjp/s13360-025-06542-3
  8. Li, D, Chen, Z, Yin, FL. A robust and secure audio zero-watermarking scheme based on novel chaotic map and dual-tree complex wavelet transform. IEEE Internet of Things J. 2025;12(15),29614-29625. https://doi.org/10.1109/JIOT.2025.3569457
  9. Zaamoune, F, Tinedert, IE, Menacer, T. Analysis of novel 3D chaotic system, hidden coexisting, adaptive control, offset boosting control, and circuit implementation. Eur J Control. 2025;84:101259. https://doi.org/10.1016/j.ejcon.2025.101259
  10. Zhou, K, Zhang, J, Xiang, J, Zhong, Y. Multi-image encryption combining four-dimensional chaotic systems and multi-layer embedding. Eur Phys J Spec Top. 2025;234(9):2827-2844. https://doi.org/10.1140/epjs/s11734-024-01321-0
  11. Bell, S, Cookson, TJ, Cope, SA, et al. Experience with variable-frequency drives and motor bearing reliability. IEEE Trans Ind Appl. 2001;37(5):1438-1446. https://doi.org/10.1109/28.952519
  12. Lai, Q, Qin, MH. Universal method for enhancing dynamics in neural networks via memristor and application in IoT-based robot navigation. IEEE Trans Cybern. 2026;56(1):557-566. https://doi.org/10.1109/TCYB.2025.3607140
  13. Khan, A, Li, C, Zhang, X, Cen, X. A two-memristor-based chaotic system with symmetric bifurcation and multistability. Chaos and Frac. 2025;2(1):1-7. https://doi.org/10.69882/adba.chf.2025011.
  14. Fan, S, Xu, X, Liu, X, Cao, Y, Gao, S, Mou, J. Complex neuronal dynamics under memristive electromagnetic radiation: Modeling and digital signal processing implementation. Non Sci and Cont Eng. 2025;1(2):025400013. https://doi.org/10.36922/NSCE025400013
  15. Yan, S, Wang, J, Zhang, J. Analysis and application of discrete 3D no equilibrium points memristive Hindmarsh-Rose models. Eur Phys J Spec Top. 2025;1-18. https://doi.org/10.1140/epjs/s11734-025-01665-1
  16. Fan, C, Ding, Q. Design and dynamic analysis of a class of new 3-D discrete memristive hyperchaotic maps with multi-type hidden attractors. Chaos, Sol & Frac. 2025;191:115905. https://doi.org/10.1016/j.chaos.2024.115905
  17. He, SQ, Yu, F, Guo, R, et al. Dynamic analysis and FPGA implementation of a fractional-order memristive Hopfield neural network with hidden chaotic dual-wing attractors. Frac & Frac. 2025;9(9):561. https://doi.org/10.3390/fractalfract9090561
  18. Kalaichelvi, K, Rameshbabu, R, Priya, VD, Rithanya, PG, Bhavadharani, GK, Gayathiri, KS. A Novel Chaotic Jerk System with Multistability and Its Circuit Implementation. Non Dy & Sys The. 2025;25(2):220. https://e-ndst.kiev.ua/v25n2/5(98).pdf
  19. Rahman, ZASA, Jasim, BH, Al-Yasir, YIA, Abd-Alhameed, RA. High-security image encryption based on a novel simple fractional-order memristive chaotic system with a single unstable equilibrium point. Elec. 2021;10(24):3130. https://doi.org/10.3390/electronics10243130
  20. Yu, F, Tan, B, He, T, et al. A wide-range adjustable conservative memristive hyperchaotic system with transient quasi-periodic characteristics and encryption application. Math. 2025;13(5):726. https://doi.org/10.3390/math13050726
  21. Wang, QM, Wang, L, Wen, W, Li, Y, Zhang, G. Dynamical analysis and preassigned-time intermittent control of memristive chaotic system via T–S fuzzy method. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2025;35(2). https://doi.org/10.1063/5.0221159
  22. Wan, ZQ, Pu, YF, Lai, Q. Memristive feedback-controlled chaotic system with diverse dynamics. Non Sci & Cont Eng. 2025;1(1):025310008. https://doi.org/10.36922/NSCE025310008
  23. Feng, XY, Lu, TA, Zhou, L. A 4D memristive chaotic system with multiple amplitude and offset controllers. Phy Scri. 2025;100(6):065237. https://doi.org/10.1088/1402-4896/add844
  24. Wang, YC, Zhang, S, Wang, Z, Wang, J, Peng, X, Hua, G. Robust Enhanced Chaos in Memristive Multi-attractor Rulkov Neuron Model with Application to Hardware Image Cryptosystem. IEEE Internet of Things J. 2025;12(15):32022-32034. https://doi.org/10.1109/jiot.2025.3575569
  25. Zhang, S, He, D, Li, Y, Lu, D, Li, C. Dual Memristor-coupled Hopfield Neural Network with Any Multi-scroll Amplitude Control and Its Application for Medical Image Classification. IEEE Trans Autom Sci Eng. 2025;22:17828-17840. https://doi.org/10.1109/TASE.2025.3585935
  26. Lai, Q, Liu, YJ, Liu, F, Zhao, XW. Generating grid multiscroll memristive Chua’s circuit and its predefined-time synchronization for secure communication. IEEE Transactions on Circuits and Systems I: Regular Papers. 2025;72(10):5947-5956. https://doi.org/10.1109/TCSI.2025.3541635
  27. Lin, YT, Liao, YL, Wei, YN, et al. Lightweight image encryption via four-dimensional Hénon memristor map and fast block permutation. Non Sci & Cont Eng. 2025;1(2):025390012. https://doi.org/10.36922/NSCE025390012
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