Abstract
In this paper, a six-neuron incommensurate fractional order BAM neural network model with multi-delays is considered. We demonstrate that the equilibrium point of the system loses its stability and Hopf bifurcation emerges when the delay passes through a critical value. And the relationship between the critical delay of Hopf bifurcation and size of fractional orders is found. Finally, some numerical simulations are given to verify the validity of the theoretical results.
Similar content being viewed by others
References
Wang P, Wang P, Fan E (2021) Neural network optimization method and its application in information processing. Math Probl Eng 1:1–10
Zheng Y, Zheng YC, Suehiro D et al (2021) Top-rank convolutional neural network and its application to medical image-based diagnosis. Pattern Recogn 120:108138
Lavin-Delgado JE, Chavez-Vazquez S, Gomez-Aguilar JF et al (2020) Fractional-order passivity-based adaptive controller for a robot manipulator type scara. Fractals 28:2040008
Liao MX, Liu YJ, Liu SN et al (2021) Stability and Hopf bifurcation of HIV-1 model with Holling II infection rate and immune delay. J Biol Dyn. https://doi.org/10.1080/17513758.2021.1895334
Aouiti C, Gharbia IB, Cao JD et al (2018) Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms. Chaos Solitons Fractals 107:111–127
Xu CJ, Liao MX, Li PL et al (2021) New results on pseudo almost periodic solutions of quaternion-valued fuzzy cellular neural networks with delays. Fuzzy Sets Syst 411:25–47
Syed Ali M, Narayanan G, Shekher V et al (2020) Global Mittag–Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays. Commun Nonlinear Sci Numer Simul 83:105088
Qi JT, Li CD, Huang TW (2014) Stability of delayed memristive neural networks with time-varying impulses. IEEE Trans Neural Netw Learn Syst 8:429–436
Xu CJ, Zhang W, Aouiti C et al (2021) Further investigation on bifurcation and their control of fractional-order bidirectional associative memory neural networks involving four neurons and multiple delays. Math Methods Appl Sci. https://doi.org/10.1002/mma.7581
Xu CJ, Liao MX, Li PL et al (2021) Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks. Chaos Solitons Fractals 142:110535
Xu CJ, Liao MX, Li PL et al (2019) Influence of multiple time delays on bifurcation of fractional-order neural networks. Appl Math Comput 361:565–582
Xu CJ, Liu ZX, Liao MX et al (2021) Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: the case of Hopf bifurcation. Math Comput Simul 182:471–494
Li XD, Fu XL, Balasubramaniam P et al (2010) Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations. Nonlinear Anal Real World Appl 11:4092–4108
Yuan J, Zhao LZ, Huang CD et al (2019) Novel results on bifurcation for a fractional-order complex-valued neural networks with leakage delay. Physica A 514:868–883
Xu CJ, Liao MX, Li PL et al (2021) Bifurcation properties for fractional order delayed BAM neural networks. Cogn Comput 13(2):322–356
Huang CD, Liu H, Shi XY et al (2020) Bifurcations in a fractional-order neural network with multiple leakage delays. Neural Netw 131:115–126
Huang CD, Zhao X, Wang XH et al (2019) Disparate delays-induced bifurcations in a fractional-order neural network. J Frankl Inst 356:2825–2846
Huang CD, Cao JD (2020) Bifurcation mechanisation of a fractional-order neural network with unequal delays. Neural Process Lett 52:1171–1187
Yu WW, Cao JD (2006) Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays. Phys Lett A 351(1–2):64–78
Xu CJ, Tang XH, Liao MX (2011) Stability and bifurcation analysis of a six-neuron BAM neural network model with discrete delays. Neurocomputing 74(5):689–707
Javidmanesh E, Dadi Z, Afsharnezhad Z et al (2014) Global stability analysis and existence of periodic solutions in an eight-neuron BAM neural network model with delays. J Intell Fuzzy Syst 27:391–406
Huang CD, Cao JD, Alofi A et al (2017) Dynamics and control in an (n + 2)-neuron BAM network with multiple delays. Nonlinear Dyn 1:313–336
Huang CD, Cao JD, Xiao M et al (2017) Controlling bifurcation in a delayed fractional predator-prey system with incommensurate orders. Appl Math Comput 293:293–310
Pan I, Das S (2015) Multi-objective active control policy design for commensurate and incommensurate fractional order chaotic financial systems. Appl Math Model 39(2):500–514
Wang X, Wang Z, Huang X et al (2018) Dynamic analysis of a fractional-order delayed SIR model with saturated incidence and treatment functions. Int J Bifurc Chaos 28(14):1850180
Podlubny I (1999) Fractional differential equations. Academic Press, New York
Deng WH, Li CP, Lu JH (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48:409–416
Matignon D (1996) Stability results for fractional differential equations with applications to control processing. Comput Eng Syst Appl 2:963–968
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supported partly by the National Natural Science Foundation of China (12261015, 61673008), Joint Fund Project of Guizhou University of Finance and Economics and Institute of International Trade and Economic Cooperation of Ministry of Commerce on Contiguous areas of extreme poverty Poor peasant psychological Poverty alleviation(2017SWBZD09), Hunan Natural Science Foundation (2020JJ4516), Hunan Provincial Key Foundation of Education Department (17A181), Hunan Key Laboratory of Mathematical Modeling and Scientific Computing.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Li, B., Liao, M., Xu, C. et al. Hopf Bifurcation Analysis of a Delayed Fractional BAM Neural Network Model with Incommensurate Orders. Neural Process Lett 55, 5905–5921 (2023). https://doi.org/10.1007/s11063-022-11118-8
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-022-11118-8