Abstract
This article analyzes the quasi-projective synchronization (QPS) issues of delayed Caputo-type BAM neural networks in the complex field. In order to facilitate calculation and realize QPS, the non-decomposition method is adopted. Moreover, a novel lemma in the form of algebraic inequality is established based on the Laplace transform, which makes it more convenient to deal with the delay term. Applying the proposed lemma, inequality techniques and Lyapunov method, some criteria of QPS are obtained via the designed different controllers. Meanwhile, the error bound is effectively derived. Eventually, the rationality of the gained criteria is tested by two simulations.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Han S, Hu C, Yu J, Jiang H, Wen S (2021) Stabilization of inertial Cohen-Grossberg neural networks with generalized delays: a direct analysis approach. Chaos, Solitons Fractals 142:110432
Zhang Z, Zhang X, Yu T (2022) Global exponential stability of neutral-type Cohen-Grossberg neural networks with multiple time-varying neutral and discrete delays. Neurocomputing 490:124–131
He X, Li X, Song S (2022) Finite-time stability of state-dependent delayed systems and application to coupled neural networks. Neural Netw 154:303–309
Lee SH, Park MJ, Ji DH, Kwon OM (2022) Stability and dissipativity criteria for neural networks with time-varying delays via an augmented zero equality approach. Neural Netw 146:141–150
Dong T, Gong X, Huang T (2022) Zero-Hopf bifurcation of a memristive synaptic Hopfield neural network with time delay. Neural Netw 149:146–156
Tu W, Zhong S, Shen Y, Incecik A, Fu X (2019) Neural network-based hybrid signal processing approach for resolving thin marine protective coating by terahertz pulsed imaging. Ocean Eng 173:58–67
Xiu C, Zhou R, Liu Y (2020) New chaotic memristive cellular neural network and its application in secure communication system. Chaos, Solitons Fractals 141:110316
Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26(23):4947–4960
Kosko B (1988) Bidirectional associative memories. IEEE Trans Syst Man Cybern Syst 18(1):49–60
Syed Ali M, Yogambigai J, Saravanan S, Elakkia S (2019) Stochastic stability of neutral-type Markovian-jumping BAM neural networks with time varying delays. J Comput Appl Math 349:142–156
Yan M, Jian J, Zheng S (2021) Passivity analysis for uncertain BAM inertial neural networks with time-varying delays. Neurocomputing 435:114–125
Xu G, Bao H (2020) Further results on mean-square exponential input-to-state stability of time-varying delayed BAM neural networks with Markovian switching. Neurocomputing 376:191–201
Kumar R, Das S (2020) Exponential stability of inertial BAM neural network with time-varying impulses and mixed time-varying delays via matrix measure approach. Commun Nonlinear Sci Numer Simul 81:105016
Zhang H, Ye R, Cao J, Alsaedie A (2018) Delay-independent stability of Riemann-Liouville fractional neutral-type delayed neural networks. Neural Process Lett 47:427–442
Gokul P, Rakkiyappan R (2022) New finite-time stability for fractional-order time-varying time-delay linear systems: a lyapunov approach. J Franklin Inst 359:7620–7631
Yang Z, Zhang J, Zhang Z, Mei J (2023) An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays. Math Comput Simul 203:910–925
Lu Q, Zhu Y (2022) Finite-time stability in measure for nabla uncertain discrete linear fractional order systems. Math Sci. https://doi.org/10.1007/s40096-022-00484-y
Syed Ali M, Narayanan G, Sevgen S, Shekher V, Arik S (2019) Global stability analysis of fractional-order fuzzy BAM neural networks with time delay and impulsive effects. Commun Nonlinear Sci Numer Simul 78:104853
Du F, Lu JG (2021) New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays. Chaos, Solitons Fractals 151:111225
Huang C, Wang J, Chen X, Cao J (2021) Bifurcations in a fractional-order BAM neural network with four different delays. Neural Netw 141:344–354
Li H, Hu C, Zhang L, Jiang H, Cao J (2022) Complete and finite-time synchronization of fractional-order fuzzy neural networks via nonlinear feedback control. Fuzzy Sets Syst 443:50–69
Hui M, Wei C, Zhang J, Ho-Ching IuH, Yao R, Bai L (2023) Finite-time synchronization of fractional-order memristive neural networks via feedback and periodically intermittent control. Commun Nonlinear Sci Numer Simul 116:106822
Zheng B, Wang Z (2022) Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays. Appl Math Comput 430:127303
Zhang H, Wang C, Zhang W, Zhang HM (2022) Mittag-Leffler stability and synchronization for FOQVFNNs including proportional delay and Caputo derivative via fractional differential inequality approach. Comput Appl Math 41:344
Wu X, Liu S, Wang H (2022) Asymptotic stability and synchronization of fractional delayed memristive neural networks with algebraic constraints. Commun Nonlinear Sci Numer Simul 114:106694
Luo T, Wang Q, Jia Q, Xu Y (2022) Asymptotic and finite-time synchronization of fractional-order multiplex networks with time delays by adaptive and impulsive control. Neurocomputing 493:445–461
Zhang H, Cheng J, Zhang HM, Zhang W, Cao J (2021) Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays. Chaos, Solitons Fractals 152:111432
Zhang H, Cheng Y, Zhang W, Zhang HM (2023) Time-dependent and Caputo derivative order-dependent quasi-uniform synchronization on fuzzy neural networks with proportional and distributed delays. Math Comput Simul 203:846–857
Zhang Y, Deng S (2019) Finite-time projective synchronization of fractional-order complex-valued memristor-based neural networks with delay. Chaos, Solitons Fractals 128:176–190
Cheng Y, Hu T, Xu W, Zhang X, Zhong S (2022) Fixed-time synchronization of fractional-order complex-valued neural networks with time-varying delay via sliding mode control. Neurocomputing 505:339–352
Song X, Sun X, Man J, Song S, Wu Q (2021) Synchronization of fractional-order spatiotemporal complex-valued neural networks in finite-time interval and its application. J Franklin Inst 358:8207–8225
Zhang H, Ye M, Ye R, Cao J (2018) Synchronization stability of Riemann-Liouville fractional delay-coupled complex neural networks. Phys A 508:155–165
Li H, Hu C, Cao J, Jiang H, Alsaedi A (2019) Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw 118:102–109
Cheng J, Zhang H, Zhang W, Zhang HM (2022) Quasi-projective synchronization for Caputo type fractional-order complex-valued neural networks with mixed delays. Int J Control Autom Syst 20(5):1723–1734
Yan H, Qiao Y, Duan L, Miao J (2022) New results of quasi-projective synchronization for fractional-order complex-valued neural networks with leakage and discrete delays. Chaos, Solitons Fractals 159:112121
Zhang H, Cheng Y, Zhang HM, Zhang W, Cao J (2022) Hybrid control design for Mittag-Leffler projective synchronization of FOQVNNs with multiple mixed delays and impulsive effects. Math Comput Simul 197:341–357
Chen S, Li H, Bao H, Zhang L, Jiang H, Li Z (2022) Global Mittag-Leffler stability and synchronization of discrete-time fractional-order delayed quaternion-valued neural networks. Neurocomputing 511:290–298
Shafiya M, Nagamani G, Dafik D (2022) Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality. Math Comput Simul 191:168–186
Yang J, Li H, Yang J, Zhang L, Jiang H (2022) Quasi-synchronization and complete synchronization of fractional-order fuzzy BAM neural networks via nonlinear control. Neural Process Lett 54:3303–3319
Wang C, Zhang H, Stamova I, Cao J (2023) Global synchronization for BAM delayed reaction-diffusion neural networks with fractional partial differential operator. J Franklin Inst 360(1):635–656
Yang J, Li H, Zhang L, Hu C, Jiang H (2023) Quasi-projective and finite-time synchronization of delayed fractional-order BAM neural networks via quantized control. Math Methods Appl Sci 46(1):197–214
Podlubny I (1999) Fractional differential equations. Academic, San Diego
Zhang W, Zhang H, Cao J, Zhang HM, Chen D (2020) Synchronization of delayed fractional-order complex-valued neural networks with leakage delay. Phys A 556:124710
Zheng B, Wang Z (2022) Adaptive synchronization of fractional-order complex-valued coupled neural networks via direct error method. Neurocomputing 486:114–122
Hu T, He Z, Zhang X, Zhong S (2020) Finite-time stability for fractional-order complex-valued neural networks with time delay. Appl Math Comput 365:124715
Cheng Y, Zhang H, Stamova I, Cao J (2023) Estimate scheme for fractional order-dependent fixed-time synchronization on Caputo quaternion-valued BAM network systems with time-varying delays. J Franklin Inst 360(3):2379–2403
Zhang H, Wang C, Ye R, Stamova I, Cao J (2023) Novel order-dependent passivity conditions of fractional generalized Cohen-Grossberg neural networks with proportional delays. Commun Nonlinear Sci Numer Simul 120:107155
Acknowledgements
This work was supported by the National Natural Science Foundation of China (61833005) and the Natural Science Foundation of Anhui Province of China (1908085MA01).
Author information
Authors and Affiliations
Contributions
XC: Writing-original draft, Software. HZ: Conceptualization, Methodology. RY: Methodology, Writing-review & editing. QL: Validation, Writing-review & editing. JC: Supervision, Project administration.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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
Chen, X., Zhang, H., Ye, R. et al. Quasi-projective Synchronization Analysis of Delayed Caputo-Type BAM Neural Networks in the Complex Field. Neural Process Lett 55, 7469–7492 (2023). https://doi.org/10.1007/s11063-023-11269-2
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-023-11269-2