A new 2D Hindmarsh-Rose neuron, its circuit implementation, and its application in dynamic flexible job shops problem

doi:10.1088/1674-1056/ae0892

Abstract We propose a simplified version of the classic two-dimensional Hindmarsh-Rose neuron (2DHR), resulting in a new 2DHR that exhibits novel chaotic phenomena. Its dynamic characteristics are analyzed through bifurcation diagrams, Lyapunov exponent spectra, equilibrium points, and phase diagrams. Based on this system, a corresponding circuit is designed and circuit simulations are carried out, yielding results consistent with the numerical simulations. To explore practical applications of chaotic systems, 2DHR is employed to improve the solution of the flexible job-shop scheduling problem with dynamic events. The research results demonstrate that applying 2DHR can significantly enhance the convergence rate of the optimization algorithm and improve the quality of the scheduling solution.

Keywords: chaos nervous system meta-heuristic algorithm dynamic flexible job-shop scheduling problem

Received: 11 July 2025
Revised: 13 September 2025
Accepted manuscript online: 18 September 2025

PACS:	05.45.Gg	(Control of chaos, applications of chaos)
	87.19.ll	(Models of single neurons and networks)
	89.75.-k	(Complex systems)

Fund: This work was supported by the Graduate Research Fund of Guizhou Province (Grant No. 2024YJSKYJJ165), the National Natural Science Foundation of China (Grant No. 62061008), and the Guizhou Provincial Basic Research Program (Natural Science) (Grant No. Qian Ke He Ji Chu-ZK [2024] General 439).

Corresponding Authors: Xianming Wu
E-mail: jsdxwxm@126.com

Cite this article:

Yao Lu(卢尧), Weijie Nie(聂伟杰), Xu Wang(王旭), Xianming Wu(吴先明), and Qingyao Ma(马晴瑶) A new 2D Hindmarsh-Rose neuron, its circuit implementation, and its application in dynamic flexible job shops problem 2025 Chin. Phys. B 34 120503

[1] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[2] Hindmarsh J and Rose R 1982 Nature 296 162
[3] Hindmarsh J and Rose R 1984 Proc. R. Soc. B 221 87
[4] Cai J, Bao H, Chen M, Xu Q and Bao B 2022 IEEE Trans. Circuits Syst. I Regul. Pap. 69 2916
[5] Linaro D, Poggi T and Storace M 2010 Phys. Lett. A 374 4589
[6] Innocenti G, Morelli A, Genesio R and Torcini A 2007 Chaos 17 043103
[7] Shilnikov A and Kolomiets M 2008 Int. J. Bifurcat. Chaos 18 2141
[8] Storace M, Linaro D and Lange E 2008 Chaos 18 033128
[9] Li B, Liang H and He Q 2021 Chaos Solitons Fractals 146 110856
[10] Bao B, Hu A, Bao H, Xu Q, Chen M and Wu H 2018 Complexity 2018 3872573
[11] Vijay S D, Thamilmaran K and Ahamed A I 2023 Nonlinear Dyn. 111 789
[12] Wang Y 2022 Phys. Scr. 97 075202
[13] Njitacke Z T, Fozin T F, Muni S S, et al. 2022 AEU Int. J. Electron. Commun. 155 154361
[14] Xie Y, Kang Y, Liu Y, et al. 2014 Sci. China Technol. Sci. 57 914
[15] Yang Y and Liao X 2018 IEEE Trans. Neural Netw. Learn. Syst. 30 306
[16] Li Z, Xie W, Zeng J and Zeng Y 2023 Chin. Phys. B 32 010503
[17] Rajagopal K, Khalaf A J M, Parastesh F, et al. 2019 Nonlinear Dyn. 98 477
[18] Guo Z, Li Z, Wang M and Ma M 2023 Chin. Phys. B 32 038701
[19] Belykh V N, Osipov G V, Petrov V S, et al. 2008 Chaos 18 037106
[20] Malik S A and Mir A H 2020 Neural Netw. 123 372
[21] Fan C, Wang W and Tian J 2024 J. Manuf. Syst. 74 180
[22] Zhang Y, Yao X and Xu S 2024 J. Mech. Sci. Technol. 38 5581
[23] Xu Y, Wang D, Zhang M, Yang M and Liang C 2025 Swarm Evol. Comput. 93 101836
[24] Plan J L and Yorke J A 1979 In: Functional Differential Equations and Approximation of Fixed Points (Springer)
[25] Baykasoglu A, Madeno glu F S and Hamzadayı A 2020 J. Manuf. Syst. 56 425
[26] Duan J and Wang J 2022 Expert Syst. Appl. 203 117489
[27] Li Y, Tao Z, Wang L, Du B, Guo J and Pang S 2023 Rob. Comput. Integr. Manuf. 79 102443

[1]	Chaos of cavity optomechanical system with Coulomb coupling Yingjia Yang(杨应佳), Liwei Liu(刘利伟), Lianchun Yu(俞连春), Weizheng Kong(孔伟正), Haiyan Jiao(焦海燕), Xiaoyan Deng(邓小燕), and Xiaoyong Li(李小勇). Chin. Phys. B, 2025, 34(8): 080503.
[2]	Complexity dynamics analysis of a dual-channel green supply chain with government intervention and cap-and-trade regulation Yuhao Zhang(张玉豪), Lin Huang(黄林), and Man Yang(杨满). Chin. Phys. B, 2025, 34(7): 070501.
[3]	Resonant tunneling diode cellular neural network with memristor coupling and its application in police forensic digital image protection Fei Yu(余飞), Dan Su(苏丹), Shaoqi He(何邵祁), Yiya Wu(吴亦雅), Shankou Zhang(张善扣), and Huige Yin(尹挥戈). Chin. Phys. B, 2025, 34(5): 050502.
[4]	Model-free prediction of chaotic dynamics with parameter-aware reservoir computing Jianmin Guo(郭建敏), Yao Du(杜瑶), Haibo Luo(罗海波), Xuan Wang(王晅), Yizhen Yu(于一真), and Xingang Wang(王新刚). Chin. Phys. B, 2025, 34(4): 040505.
[5]	Study and circuit design of stochastic resonance system based on memristor chaos induction Qi Liang(梁琦), Wen-Xin Yu(于文新), and Qiu-Mei Xiao(肖求美). Chin. Phys. B, 2025, 34(4): 040502.
[6]	Hybrid image encryption scheme based on hyperchaotic map with spherical attractors Zhitang Han(韩智堂), Yinghong Cao(曹颖鸿), Santo Banerjee, and Jun Mou(牟俊). Chin. Phys. B, 2025, 34(3): 030503.
[7]	Impact of the chaotic semiconductor laser output power on time-delay-signature of chaos and random bit generation Chenpeng Xue(薛琛鹏), Xu Wang(王绪), Likai Zheng(郑利凯), Haoyu Zhang(张昊宇), Yanhua Hong, and Zuxing Zhang(张祖兴). Chin. Phys. B, 2025, 34(3): 030504.
[8]	A novel variable-order fractional chaotic map and its dynamics Zhouqing Tang(唐周青), Shaobo He(贺少波), Huihai Wang(王会海), Kehui Sun(孙克辉), Zhao Yao(姚昭), and Xianming Wu(吴先明). Chin. Phys. B, 2024, 33(3): 030503.
[9]	Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation Xiaodong Zhang(张晓东), Jiongning Che(车炯宁), and Barbara Dietz. Chin. Phys. B, 2024, 33(12): 120501.
[10]	On fractional discrete financial system: Bifurcation, chaos, and control Louiza Diabi, Adel Ouannas, Amel Hioual, Shaher Momani, and Abderrahmane Abbes. Chin. Phys. B, 2024, 33(10): 100201.
[11]	Critical dispersion of chirped fiber Bragg grating for eliminating time delay signature of distributed feedback laser chaos Da-Ming Wang(王大铭), Yi-Hang Lei(雷一航), Peng-Fei Shi(史鹏飞), and Zhuang-Ai Li(李壮爱). Chin. Phys. B, 2023, 32(9): 090505.
[12]	A novel fractional-order hyperchaotic complex system and its synchronization Mengxin Jin(金孟鑫), Kehui Sun(孙克辉), and Shaobo He(贺少波). Chin. Phys. B, 2023, 32(6): 060501.
[13]	Unstable periodic orbits analysis in the Qi system Lian Jia(贾莲), Chengwei Dong(董成伟), Hantao Li(李瀚涛), and Xiaohong Sui(眭晓红). Chin. Phys. B, 2023, 32(4): 040502.
[14]	An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[15]	Dynamic modelling and chaos control for a thin plate oscillator using Bubnov-Galerkin integral method Xiaodong Jiao(焦晓东), Xinyu Wang(王新宇), Jin Tao(陶金), Hao Sun(孙昊) Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(11): 110504.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

A new 2D Hindmarsh-Rose neuron, its circuit implementation, and its application in dynamic flexible job shops problem

Cite this article:

Online attention