-
近年来，基于忆阻器的突触串扰模拟研究虽取得显著进展，但现有模型仍多采用单一忆阻器结构，难以同时有效表征兴奋性与抑制性突触连接，也无法充分捕捉生物神经元的记忆效应与非局部特征。为此，本研究提出一种分数阶忆阻桥突触串扰耦合模型，通过融合Hindmarsh-Rose（HR）与FitzHugh-Nagumo（FN）神经元，构建新型基于分数阶微积分的8维异质耦合神经网络模型——分数阶忆阻桥式串扰耦合神经网络（FMBCCNN）。该模型的核心创新在于引入分数阶忆阻桥结构，兼具历史记忆特性与突触权重的双向调控能力，突破了传统耦合形式的约束。我们系统分析了传统与非均匀分数阶条件下，突触强度与串扰强度对放电活动的影响，借助时间序列、相图、分岔图与李雅普诺夫指数等多种方法，揭示了系统丰富的动力学行为，包括吸引子共存、倍周期分岔和混沌危机等现象。同时模拟了分数阶导数变化的影响，为神经元放电现象提供了更广义的表征。最终，将该系统生成的混沌序列应用于基于位平面分解与DNA编码的图像加密算法中。安全性分析表明，图像加密后水平、垂直和对角三个方向上的像素相关性皆远小于0.01，信息熵达到7.999以上，密钥空间为22080，因此所提方法与序列具备良好的加密性能与可靠性。Recent advances in crosstalk simulation using integer-order memristive synapses have shown considerable progress. However, most existing models still employ a single-memristor structure, which constrains synaptic weight modulation and makes it difficult to represent both excitatory and inhibitory synaptic connections in a unified manner. These models also often fail to capture the memory effects and nonlocal dynamic properties inherent in biological neurons. To address these issues, this study introduces a fractional-order memristive bridge synapse model for crosstalk coupling. By combining Hindmarsh–Rose (HR) and FitzHugh–Nagumo (FN) neurons, we construct an 8D heterogeneous coupled neural network based on fractional calculus—designated as the Fractional-Order Memristive Bridge Crosstalk-Coupled Neural Network (FMBCCNN). A major innovation is the incorporation of a fractional-order memristive bridge structure that mimics synaptic connections in a bridge configuration. This design provides both historical memory characteristics and bidirectional synaptic weight regulation, overcoming limitations of traditional coupling forms.
Using dynamical analysis tools such as phase portraits, bifurcation diagrams, and Lyapunov exponents, we systematically investigate how synaptic and crosstalk strengths influence system behavior under conventional fractional-order conditions. The results reveal diverse dynamical behaviors, including attractor coexistence, forward and reverse period-doubling bifurcations, and chaotic crises. Further analysis under the more generalized condition of non-uniform fractional orders shows that, compared with the conventional case, the system maintains continuous periodic motion over broader parameter ranges and exhibits clear parameter hysteresis. Although local dynamic patterns remain similar, the corresponding parameter intervals are substantially widened. In addition, the system displays more concentrated and marked alternation between periodic and chaotic behaviors. We also simulate the effect of varying the fractional-order derivative, offering a more general mathematical characterization of neuronal firing activity.
Finally, the chaotic sequences generated by the system are applied to an image encryption algorithm incorporating bit-plane decomposition and DNA encoding. Security analysis confirms that the encrypted images have pixel correlation coefficients below 0.01 in horizontal, vertical, and diagonal directions, information entropy greater than 7.999, and a key space of 22080. These results verify the excellent encryption performance and reliability of the proposed scheme and the generated sequences.-
Keywords:
- Memristive bridge /
- synaptic crosstalk /
- fractional-order heterogeneous neural network /
- nonlinear dynamics
-
[1] Sun H N, Tian H X, Hu Y H, Cui Y, Chen X R, Xu M Y, Wang X F, Zhou T 2024 Advanced Science 11 2406242
[2] Bernardo V M, Jordi M, Mireya Z 2024 Frontiers in Neuroscience 18 1425861
[3] Shan H X, Wei C Y, Ramos N, Yang X X, Guo C, Li H, Chen Y R 2025 Artificial Intelligence Science and Engineering 1 17
[4] Yuan Y, Liu J, Zhao P, Huo H, Fang T 2021 Journal of Theoretical Biology 526 110811
[5] Wang B C, Ren G D, Ma J, Guo Y T 2025 Chaos, Solitons & Fractals 198 116630
[6] John E P, Kevin M S 2023 Dynamics 3 282
[7] Johnson M G, Chartier S 2017 The quantitative methods for psychology 13 105
[8] Sun H G, Zhang Y, Baleanu D, Chen W, Yang-Quan C 2018 Communications in Nonlinear Science and Numerical Simulation 64 213
[9] Anjapuli P S, Venkatesan G 2024 Mathematical Methods in the Applied Sciences 47 2177
[10] Zhu W Y, Pu Y F, Liu B, Yu B, Zhou J L 2022 Chinese Physics B 31 060204
[11] Ding D W, Jin F, Zhang H W, Yang Z L, Chen S Q, Zhu H F, Xu X Y, Liu X 2024 Chaos, Solitons & Fractals 187 115397
[12] Lu Y M, Wang C H, Deng Q L, Xu C 2022 Chinese physics B 31 060502
[13] Wang C H, Li Y F, Deng Q L 2025 Chaos, Solitons & Fractals 193 116053
[14] He S B, Vignesh D, Rondoni L, Banerjee S 2023 Neural Networks 167 572
[15] Jin B Y, Wang Z L, Wang T Y, Meng J L 2025 Research 8 0758
[16] Lai Q, Chen Y D 2023 Chaos: An Interdisciplinary Journal of Nonlinear Science 33 083149
[17] Ding S K, Wang N, Bao H, Chen B, Wu H G, Xu Q 2023 Chaos, Solitons & Fractals 166 112899
[18] Feng B S, Liu Z Y 2025 Nonlinear Dynamics 113 23521
[19] Ding D W, Chen S Q, Zhang H W, Yang Z L, Jin F, Liu X 2024 Nonlinear Dynamics 112 10529
[20] Pu Y F, Yu B, He Q Y, Yuan X 2021 Frontiers of Information Technology & Electronic Engineering 22 862
[21] Ma M L, Xiong K L, Li Z J, He S B 2024 Chinese Physics B 33 028706
[22] Wang X, Du J R, Li Z J, Ma M L, Li C L 2024 Acta Phys. Sin. 73 110503 (in Chinese) [王璇, 杜健 嵘, 李志军, 马铭磷, 李春来 2024 物理学报 73 110503]
[23] Ding D W, Wang M Y, Wang J, Yang Z L, Niu Y, Wang W 2024 Acta Phys. Sin. 73 100502 (in Chinese) [丁大为, 王谋媛, 王金, 杨宗立, 牛炎, 王威 2024 物理学报 73 100502]
[24] Ding D W, Lu X Q, Hu Y B, Yang Z L, W, Zhang H W 2022 Acta Phys. Sin. 71 230501 (in Chinese) [丁大为, 卢小齐, 胡永兵, 杨宗立, 王威, 张红伟 2022 物理学报 71 230501]
[25] Li Z J, Peng C, Wang M J, Ma M L 2024 Indian Journal of Physics 98 1043
[26] Wang Z C, Ma Y X, Wang Y F, Sun J W 2023 Journal of Electronics & Information Technology 45 9 (in Chinese) [王子成, 马永幸, 王延峰, 孙军伟 2023 电子与信息学报 45 9]
[27] Liu D H, Wang K H, Cao Y H, Lu J S 2024 Electronics 13 2776
[28] Li Y Q, Liang Y, Jin P P, Wang S C, Wang G Y 2025 IEEE Transactions on Consumer Electronics 71 1249
[29] Qiu R, Dong Y J, Jiang X, Wang G Y 2022 Electronics 11 3034
[30] Zhang S H, Zhang H L, Wang C, Lin H R 2024 Chaos, Solitons & Fractals 179 114459
[31] Shamsi J, Mara Jose A, Bernabe L B, Teresa S G 2021 Frontiers in Neuroscience 15 674567
[32] Zhang H W, Fu C L, Pan Z X, Ding D W, Wang J, Yang Z L, Liu T 2024 Acta Phys. Sin. 73 180501 (in Chinese) [张红伟, 付常磊, 潘志翔, 丁大为, 王金, 杨宗立, 刘涛 2024 物理学报 73 180501]
[33] Akif A, Mustafa Y, Berkay E 2025 Integration 102 102355
[34] Yu F, Su D, He S Q, Wu Y Y, Zhang S K, Yin H G 2025 Chinese Physics B 34 050502
[35] Chai X L, Fu X L, Gan Z H, Lu Y, Chen Y R 2019 Signal Processing 155 44
[36] Moatsum A, Azman S, Je Sen T, Rami S A 2019 Signal Processing 160 45
[37] Yan X P, Wang X Y, Xian Y J 2021 Multimedia Tools and applications 80 10949
[38] He J H 2023 Research on Multiple Image Encryption Algorithm Based on Chaos and DNA Coding. Master’s thesis, Inner Mongolia: Inner Mongolia University of Science and Technology (in Chinses) [何纪辉 2023 硕士学位论文 (内蒙古：内蒙古科技大学)]
[39] Lin H R, Duan C X, Deng X H, Min G 2025 Journal of Electronics & Information Technology 47 1 (in Chinese) [蔺海荣, 段晨星, 邓晓衡, GeyongMin 2025 电子与信息学报 47 1]
[40] Hong Q H, Zhao L, Wang X P 2019 Neurocomputing 330 11
[41] Alon A, Fernando C, Ronald T 2016 International Journal of Circuit Theory and Applications 44 127
[42] Kim H, Sah M P, Yang C J, Roska T, Chua L O 2012 Proceedings of the IEEE 100 2061
[43] Yao P, Wu H Q, Gao B, Eryilmaz S B, Huang X Y, Zhang W Q, Zhang Q T, Deng N, Shi L P, Wong H S P, Qian H 2017 Nature communications 8 15199
[44] K U, PA S 2019 Biosystems 178 1
[45] Fang X Y, Duan S K, Wang L D 2023 Neurocomputing 517 93
[46] Farideh G, Rezvan G, Nasser S 2023 Fractal and Fractional 7 245
[47] Zhao H M, Yang H G, Chen J J, Jiang P, Zeng Z G 2025 Chaos, Solitons & Fractals 199 116588
[48] Jie J F, Wang Q Y, Zhang P, Li D Q, Yang Y 2025 Nonlinear Dynamics 113 13859
计量
- 文章访问数: 7
- PDF下载量: 0
- 被引次数: 0
下载:
