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2023, 03, v.22;No.86 56-71+94
基于反馈控制的分数阶复值神经网络的Hopf分岔
基金项目(Foundation): 国家自然科学基金面上项目(61374011);; 山东省自然科学基金面上项目(ZR2020MF080)
邮箱(Email):
DOI: 10.12194/j.ntu.20221128004
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摘要:

研究了具有时滞的分数阶复值神经网络的分岔控制问题。通过对原系统设计反馈控制器,调节反馈增益参数来改善系统的动态性能,并产生Hopf分岔;给出了系统产生Hopf分岔的充分条件和临界参数值;最后通过数值仿真验证了理论结果的正确性。

Abstract:

This study investigates the bifurcation control problem of fractional complex-valued neural networks with time delays. By designing a feedback controller for the original system and adjusting the feedback gain parameters,the dynamic performance of the system is improved, and a Hopf bifurcation is generated. The sufficient conditions for the system to exhibit Hopf bifurcation and the critical parameter values are provided. Finally, the theoretical results is verified through numerical simulations.

参考文献

[1] LIU H J, ZHANG J R, LIU Q S, et al. Minimum spanning tree based graph neural network for emotion classification using EEG[J]. Neural Networks:the Official Journal of the International Neural Network Society, 2022, 145:308-318.

[2] LI M, HONG Q H, WANG X P. Memristor-based circuit implementation of Competitive Neural Network based on online unsupervised Hebbian learning rule for pattern recognition[J]. Neural Computing and Applications, 2022,34(1):319-331.

[3]李超波,李洪均,徐晨.深度学习在图像识别中的应用[J].南通大学学报(自然科学版),2018, 17(1):1-9.LI C B, LI H J, XU C. Application of deep learning in image recognition[J]. Journal of Nantong University(Natural Science Edition), 2018, 17(1):1-9.(in Chinese)

[4] MA Z L, LI X J. Data-driven fault detection for largescale network systems:a mixed optimization approach[J].Applied Mathematics and Computation, 2022, 426:127134.

[5]邢广霞,高岩波.带有时变时滞的递归神经网络的稳定性分析[J].南通大学学报(自然科学版),2015, 14(3):12-20.XING G X, GAO Y B. Stability analysis for recurrent neural networks with time-varying delay[J]. Journal of Nantong University(Natural Science Edition), 2015, 14(3):12-20.(in Chinese)

[6] WANG T S, WANG Y, CHENG Z S. Stability and Hopf bifurcation analysis of a general tri-diagonal BAM neural network with delays[J]. Neural Processing Letters, 2021, 53(6):4571-4592.

[7] ESKANDARI Z, ALIDOUSTI J, AVAZZADEH Z, et al.Dynamics and bifurcations of a discrete time neural network with self connection[J]. European Journal of Control,2022, 66:100642.

[8]陆双,高岩波.带有时变时滞的惯性神经网络的同步[J].南通大学学报(自然科学版),2020, 19(1):83-94.LU S, GAO Y B. Synchronization of inertial neural networks with time-varying delays[J]. Journal of Nantong University(Natural Science Edition), 2020, 19(1):83-94.(in Chinese)

[9] ZHOU S, XIAO M, WANG L, et al. Bifurcation and oscillations of a multi-ring coupling neural network with discrete delays[J]. Cognitive Computation, 2021, 13(5):1233-1245.

[10] XU C J, LIAO M X, LI P L, et al. Influence of multiple time delays on bifurcation of fractional-order neural networks[J]. Applied Mathematics and Computation, 2019, 361:565-582.

[11]徐国雄,包海波.时滞分数阶递归神经网络的输入状态稳定性[J].南通大学学报(自然科学版),2020, 19(1):62-67.XU G X, BAO H B. Input-to-state stability of fractional order recurrent neural networks with delays[J]. Journal of Nantong University(Natural Science Edition), 2020, 19(1):62-67.(in Chinese)

[12] HUANG C D, CAO J D. Bifurcations induced by selfconnection delay in high-order fractional neural networks[J]. Neural Processing Letters, 2021, 53(1):637-651.

[13] XU C J, LIU Z X, LIAO M X, et al. Fractional-order bidirectional associate memory(BAM)neural networks with multiple delays:the case of Hopf bifurcation[J]. Mathematics and Computers in Simulation, 2021, 182:471-494.

[14] VELMURUGAN G, RAKKIYAPPAN R, VEMBARASAN V, et al. Dissipativity and stability analysis of fractionalorder complex-valued neural networks with time delay[J].Neural Networks, 2017, 86:42-53.

[15] TAN M C, PAN Q. Global stability analysis of delayed complex-valued fractional-order cou pled neural networks with nodes of different dimensions[J]. International Journal of Machine Learning and Cybernetics, 2019, 10(5):897-912.

[16] HUANG C D, CAO J D, XIAO M, et al. Bifurcations in a delayed fractional complex-valued neural network[J]. Applied Mathematics and Computation, 2017, 292:210-227.

[17] YUAN J, ZHAO L Z, HUANG C D, et al. Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay[J]. Physica A:Statistical Mechanics and Its Applications, 2019, 514:868-883.

[18] ZHANG L, SONG Q K, ZHAO Z J. Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays[J]. Applied Mathematics and Computation, 2017, 298:296-309.

[19] WANG X H, WANG Z, ZHU X G, et al. Stability and Hopf bifurcation of fractional-order complex-valued neural networks with time-delay[J]. IEEE Access, 2019, 7:158798-158807.

[20] XIAO M, ZHENG W X, LIN J X, et al. Fractional-order PD control at Hopf bifurcations in delayed fractional-order small-world networks[J]. Journal of the Franklin Institute,2017, 354(17):7643-7667.

[21] HUANG C D, CAO J D, XIAO M. Hybrid control on bifurcation for a delayed fractional gene regulatory network[J]. Chaos, Solitons&Fractals, 2016, 87:19-29.

[22] SINGH A, RAI J N. Stability of fractional order fuzzy cellular neural networks with distributed delays via hybrid feedback controllers[J]. Neural Processing Letters, 2021,53(2):1469-1499.

[23] CHEN G R, MOIOLA J L, WANG H O. Bifurcation control:theories, methods, and applications[J]. International Journal of Bifurcation and Chaos, 2000, 10(3):511-548.

基本信息:

DOI:10.12194/j.ntu.20221128004

中图分类号:TP183

引用信息:

[1]宋倩倩,程尊水.基于反馈控制的分数阶复值神经网络的Hopf分岔[J],2023,22(03):56-71+94.DOI:10.12194/j.ntu.20221128004.

基金信息:

国家自然科学基金面上项目(61374011);; 山东省自然科学基金面上项目(ZR2020MF080)

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