AccScience Publishing / NSCE / Online First / DOI: 10.36922/NSCE025310008
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Memristive feedback-controlled chaotic system with diverse dynamics

Zhiqiang Wan1 ,  Yi-Fei Pu1* ,  Qiang Lai2
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1 College of Computer Science, Sichuan University, Chengdu, China
2 School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, China
NSCE, 025310008 https://doi.org/10.36922/NSCE025310008
Received: 23 July 2025 | Revised: 20 August 2025 | Accepted: 28 August 2025 | Published online: 8 September 2025
© 2025 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 construction of chaotic systems exhibiting diverse dynamics has long been a research focus in nonlinear science. The emergence of memristors with strong nonlinear characteristics introduces new design perspectives for developing such systems. This study introduces a memristor involving trigonometric functions into a nonlinear system via feedback control, resulting in the construction of a memristive chaotic system with rich dynamics. The equilibrium points and their stability are thoroughly analyzed under the given conditions. Numerical investigations reveal that the system exhibits an unusual bifurcation behavior, wherein the state variables can reside in different bifurcation states under the same bifurcation parameter along the period-doubling route. In addition, a single system parameter allows for sensitive amplitude regulation of all chaotic states. A time-driven nested attractor is also observed in the system, which gradually develops a nested structure over time and extends infinitely in a specific direction within the phase space. A Multisim-based analog equivalent circuit is designed to implement the proposed system, thereby validating its physical feasibility.

Keywords
Chaos
Memristor
Bifurcation dynamics
Amplitude controllability
Chaotic circuit
Funding
This work was supported by the National Natural Science Foundation of China under Grants 62171303.
Conflict of interest
The authors declare they have no competing interests.
References
  1. Kumbhakar R, Karmakar S, Pal N, Kurths J. Shrimp-shapedstructure and period-bubbling route to chaos in aone-dimensional economic model. Chaos. 2024;34(10): 103115.

 

  1. Ryashko L. Multistability, infection-induced bifurcations andchaos in a discrete population model with treatment. Int J BifurChaos. 2025;35(6):25500749. https://doi.org/10.1142/S0218127425500749.

 

  1. Tamba VK, Ngoko G, Pham VT, Grassi G. Chaos, hyperchaosand transient chaos in a 4D Hopfield neural network:numerical analyses and PSpice implementation. Math.2025;13(11):1872.

 

  1. Hamidouche B, Guesmi K, Essounbouli N. Mastering chaos: areview. Annu Rev Cont. 2024;58:100966.

 

  1. Karimov A, Rybin V, Babkin I, Karimov T, Ponomareva V,Butusov D. Time-reversible synchronization of analog anddigital chaotic systems. Math. 2025;13(9):1437.

 

  1. Hua Z, Wu Z, Zhang Y, Bao H, Zhou Y. Two-dimensionalcyclic chaotic system for noise-reduced OFDM-DCSKcommunication. IEEE Trans Circuits Syst I, Reg Papers.2025;72(1):323-336.

 

  1. Nabil H, Tayeb H. A fractional-order chaotic Lorenz-basedchemical system: dynamic investigation, complexityanalysis, chaos synchronization, and its application tosecure communication. Chin Phys B. 2024;33(12): 120503.

 

  1. Tang J, Zhang Z, Huang T. Two-dimensional cosine-sineinterleaved chaotic system for secure communication. IEEETrans Circuits Syst II, Exp Briefs. 2024;71(4):2479-2483.

 

  1. Toktas A, Erkan U, Ustun D, Lai Q. Multiobjectivedesign of 2D hyperchaotic system using leader paretogrey wolf optimizer. IEEE Trans Syst Man Cyber -Sys.2024;54(9):5237-5247.

 

  1. Wei X, Zhang J, Li H, Zuo J. Nonlinear analysis, circuit design,and chaos optimisation application of multiscroll chaoticattractors based on novel locally active non-polynomialmemristor. Nonlinear Dyn. 2025;113(6): 5773-5810.

 

  1. Fetteha MA, Sayed WS, Said LA. A lightweight imageencryption scheme using DNA coding and chaos. Electronics.2023;12(24):4895.

 

  1. Peng Y, Lan Z, Li Z, Li C. An effective anti-object-detectionimage privacy protection scheme based on robust chaos. IEEETrans Indus Infor. 2024;20(5):7227-7237.

 

  1. Boya B, Nanfak A, Ngono J, Klimentyevna B, Nkapkop J, EffaY. Six-scroll chaos within the dynamics of the Thomas chaoticsystem and application to biomedical data encryption. PhysSci. 2025;100(1):015244.

 

  1. Demirkol A, Sahin M, Karakaya B, Ulutas H, Ascoli A, TetzlaffR. Real time hybrid medical image encryption algorithmcombining memristor-based chaos with DNA coding. ChaosSolit Fract. 2024;183:114923.

 

  1. Huang L, Gao H. Multi-image encryption algorithm basedon novel spatiotemporal chaotic system and fractal geometry.IEEE Trans Circuits Syst I, Reg Pap. 2024;71(8):3726-3739.

 

  1. Vivekanandhan G, Chedjou J, Jacques K, Rajagopal K. Aunique self-driven 5D hyperjerk circuit with hyperbolic sinefunction: hyperchaos with three positive exponents, complextransient behavior and coexisting attractors. Chaos Solit Fract.2024;186:115276.

 

  1. Liu W, Sun K, Wang H, Li B. Delayed feedback chaotificationmodel and its hardware implementation. IEEE Trans IndusElect. 2024;71(10):13002-13011.

 

  1. Seth S, Kudra G, Wasilewski G, Awrejcewicz J. Studythe bifurcations of a 2DoF mechanical impacting system.Nonlinear Dyn. 2023;112(3):1713-1728.

 

  1. Anzo-Hern Aandez, Zambrano-Serrano E, Platas-Garza M,Volos C. Dynamic analysis and FPGA implementation offractional-order Hopfield networks with memristive synapse.Fractal Fract. 2024;8(11):628.

 

  1. Di Marco M, Forti M, Pancioni L, Tesi A. Snap-back repellersand chaos in a class of discrete-time memristor circuits.Nonlinear Dyn. 2024;112(15):13519-13537.

 

  1. Tchiedjo S, Kengne L, Kengne J, Kenmoe G. Dynamicalbehaviors of a chaotic jerk circuit based on a novel memristivediode emulator with a smooth symmetry control. Eur Phys JPlus. 2022;137(8):940.

 

  1. Lai Q, Wan z, Kuate P. Generating grid multi-scroll attractorsin memristive neural networks. IEEE Trans Circuits Syst I, Reg.Pap. 2023;70(3):1324-1336.

 

  1. Wan z, Pu Y, Lai Q. Multiscroll hidden attractor inmemristive autapse neuron model and its memristor-basedscroll control and application in image encryption. NeuralNetw. 2025;188:107473.

 

  1. Wan Z, Pu Y, Qin M, Lai Q. Robust full parameter controlmethod: constructing multiscroll HNN via memristor. NeuralNetw. 2025;192:107878.

 

  1. Vijayakumar M, Natiq H, Meli M, Leutcho G,Njitacke Z.Hamiltonian energy computation of a novelmemristive mega-stable oscillator (MMO) with dissipative,conservative and repelled dynamics. Chaos Solit Fract.2022;155:111765.

 

  1. Yu F, Zhang W, Xiao X, et al. Dynamic analysis and FPGAimplementation of a new, simple 5D memristive hyperchaoticSprott-C system. Math. 2023;11(3): 701.

 

  1. Bao H, Li H, Hua, Xu Q, Bao B. Sine-transform-basedmemristive hyperchaotic model with hardwareimplementation. IEEE Trans Indus Infor. 2023;19( 3):2792-2801.

 

  1. Ramakrishnan B, Wang Z, Natiq H, Pal N, Rajagopal K ,Jafari S. Dynamics of a two-neuron hopfield neural network:memristive synapse and autapses and impact of fractionalorder. AEU-Int J Elect Commu. 2024; 187: 155506, 2024.

 

  1. Njitacke Z, Parthasarathy S, Takembo C, Rajagopal K,Awrejcewicz J. Dynamics of a memristive FitzHugh-Rinzelneuron model: application to information patterns. Eur Phys JPlus. 2023; 138(5):473.

 

  1. He S, Vignesh D, Rondoni L, Banerjee S. Chaos andmulti-layer attractors in asymmetric neural networkscoupled with discrete fractional memristor. Neural Netw.2023;167:572-587.

 

  1. Lai Q, Xu Y, Fortuna L. Generating simplecyclic memristive neural network circuit withcontrollable multiscroll attractors and multivariableamplitude control. IEEE Trans Neur Netw Lear Syst.2025,https://doi.org/10.1109/TNNLS.2025.3581229.

 

  1. Chen C, Gao B, Yu Y, et al. Synchronously adjustableoffset boosting and amplitude control in memristive neuralnetwork with hardware implementation. Chaos Solit Fract.2025;199:116871.

 

  1. Lalili Y, Bouden T, Grimes M, Yalcin M, Abderrazak L, ElbasiE. FPGA realization of a controllable 4-D hyperchaotic systemfor quantum-inspired medical image encryption. Phys Sci.2025;100(7):075262.

 

  1. Lai Q, Lai C, Zhang H, Li C. Hidden coexisting hyperchaosof new memristive neuron model and its application in imageencryption. Chaos Solit Fract. 2022;158:112017.

 

  1. Adhikari S, Sah M, Kim H, Chua L. Three fingerprintsof memristor. IEEE Trans Circuits Syst I, Reg Papers.2013;60(11):3008-3021.
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