Global exponential stability for generalized Cohen-Grossberg neural networks with variable delay
*Wided GouadriCorresponding authorgouadri2016@gmail.comDepartment of MathematicsFaculty of Sciences of SfaxLaboratory Stability and Control of Systems and nonlinear PDEsUniversity of SfaxBP 1171, Rte Soukra Sfax, 3000, Tunisia0009-0008-3049-1249View full profile → , Mohamed Ali Hammamimohamedali.hammami@fss.rnu.tnDepartment of MathematicsFaculty of Sciences of SfaxLaboratory Stability and Control of Systems and nonlinear PDEsUniversity of SfaxBP 1171, Rte Soukra Sfax, 3000, Tunisia0000-0002-9347-4525View full profile →
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- Received:
- 09 Apr 2025
- Published Online:
- 22 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2338
- Pages:
- 875–890
Abstract
Keywords
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References
[1] A. Meyer-Baese, S. S. Pilyugin, and Y. Chen, Global exponential stability of competitive neural networks with different time scales, IEEE Trans. Neural Netw., vol. 14, no. 3, pp. 716–719 (May 2003), doi: 10.1109/TNN.2003.810594.
[2] X. Feng, F. Zhang, and W. Wang, Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects, Chaos, Solitons Fractals, vol. 44, no. 1-3, pp. 9–16 (Jan. 2011), doi: 10.1016/j.chaos.2010.10.003.
[3] Y. V. Pershin and M. D. Ventra, Experimental demonstration of associative memory with memristive neural networks, Neural Netw., vol. 23, no. 7, pp. 881–886 (Sep. 2010), doi: 10.1016/j.neunet.2010.05.001.
[4] J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-stage neurons, Proc. Nat. Acad. Sci. USA, vol. 81, no. 10, pp. 3088–3092 (May 1984), doi: 10.1073/pnas.81.10.3088.
[5] M. A. Cohen and S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Syst., Man, Cybern., vol. SMC-13, no. 5, pp. 815–826 (Sep. 1983), doi: 10.1109/TSMC.1983.6313075.
[6] T. Huang, C. Li, and G. Chen, Stability of Cohen-Grossberg neural networks with unbounded distributed delays, Chaos, Solitons Fractals, vol. 34, no. 3, pp. 992–996 (Nov. 2007), doi: 10.1016/j.chaos.2006.04.008.
[7] B. Kosko, Bidirectional associative memories, IEEE Trans. Syst., Man, Cybern., vol. 18, no. 1, pp. 49–60 (Jan. 1988), doi: 10.1109/21.87054.
[8] K. Gopalsamy and X. Z. He, Delay-independent stability in bi-directional associative memory networks, IEEE Trans. Neural Netw., vol. 5, no. 6, pp. 998–1002 (Nov. 1994), doi: 10.1109/72.329700.
[9] M. Benjemaa, W. Gouadri, and M. A. Hammami, Novel criteria for stability and convergence of solutions for non-autonomous nonlinear systems, Mathematica, vol. 66, no. 89, pp. 1–15 (2024), doi: 10.24193/mathcluj.2024.1.05.
[10] M. Galicki, H. Witte, J. Dörschel, M. Eiselt, and G. Griessbach, Common optimization of adaptive preprocessing units and a neural network during the learning period. Application in EEG pattern recognition, Neural Netw., vol. 10, no. 6, pp. 1153–1163 (Aug. 1997), doi: 10.1016/S0893-6080(97)00033-6.
[11] M. A. Hammami, Global convergence of a control system by means of an observer, J. Optim. Theory Appl., vol. 108, no. 2, pp. 377–388 (Feb. 2001), doi: 10.1023/A:1026442402201.
[12] M. Hammi and M. A. Hammami, Gronwall-Bellman type integral inequalities and applications to global uniform asymptotic stability, Cubo, vol. 17, no. 3, pp. 53–70 (Oct. 2015), doi: 10.4067/S0719-06462015000300004.
[13] S. C. Tong, Y. M. Li, and H. G. Zhang, Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays, IEEE Trans. Neural Netw., vol. 22, no. 7, pp. 1073–1086 (Jul. 2011), doi: 10.1109/TNN.2011.2146274.
[14] J. Wang, Y. Cai, and J. Yin, Multi-start stochastic competitive Hopfield neural network for frequency assignment problem in satellite communications, Expert Syst. Appl., vol. 38, no. 1, pp. 131–145 (Jan. 2011), doi: 10.1016/j.eswa.2010.06.027.
[15] M. Benjemaa, W. Gouadri, and M. A. Hammami, Stability analysis of nonlinear systems with impulsive perturbations: Application to Hopfield neural networks, Discontinuity, Nonlinearity, Complex., vol. 11, no. 2, pp. 1–12 (2022), doi: 10.5890/DNC.2023.12.006.
[16] I. J. Mohammad and A. J. Mohammad, Neural network of multivariate Bernstein operators with positive integer parameter m, J. Interdiscip. Math., vol. 25, no. 2, pp. 1–10 (2022), doi: 10.1080/09720502.2022.2046334.
[17] R. Ma, M. Fečkan, and J. Wang, Exponential Stability of Hopfield Neural Network Model with Non-Instantaneous Impulsive Effects, Axioms, vol. 12, no. 2, pp. 1-13 (Jan. 2023), doi: 10.3390/axioms12020115.
[18] M. Norizan, H. A. Maizah, I. Zuhaimy, and A. A. Khairil, Comparing forecasting performances between multilayer feedforward neural network and recurrent neural network in Malaysia’s load, J. Interdiscip. Math., vol. 13, no. 2, pp. 125–134 (2013), doi: 10.1080/09720502.2010.10700685.
[19] M. Rhaima, L. Mchiri, N. H. Taieb, M. A. Hammami, and A. Ben Makhlouf, Practical stability of fractional-order nonlinear fuzzy systems, Int. J. Gen. Syst., vol. 52, no. 7, pp. 864–875 (2023), doi: 10.1080/03081079.2023.2219825.
[20] Z. Zhang, X. Liang, J. Lan, and X. Zhang, Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays, Math. Methods Appl. Sci., vol. 47, no. 9, pp. 7165–7181 (Jun. 2024), doi: 10.1002/mma.9962.
[21] K. Russul and M. A. A. Khalid Mindeel, Modification artificial neural networks for solving singular perturbation problems, J. Interdiscip. Math., vol. 25, no. 5, pp. 1535–1549 (2022), doi: 10.1080/09720502.2022.2072063.
[22] L. Wan, Q. Zhou, H. Fu, and Q. Zhang, Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays, AIMS Math., vol. 6, no. 8, pp. 8030–8043 (2021), doi: 10.3934/math.2021466.
[23] C. Aouiti and F. Dridi, New results on impulsive Cohen–Grossberg neural networks, Neural Process. Lett., vol. 49, no. 3, pp. 1459–1483 (Jun. 2019), doi: 10.1007/s11063-018-9880-y.
[24] J. Cao, New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Phys. Lett. A, vol. 307, no. 2-3, pp. 136–147 (Mar. 2003), doi: 10.1016/S0375-9601(02)01720-6.
[25] F. Delmotte, M. A. Hammami, and A. Jellouli, Exponential stabilization of fuzzy systems with perturbations by using state estimation, Int. J. Gen. Syst., vol. 50, no. 4, pp. 388–408 (2021), doi: 10.1080/03081079.2021.1907366.
[26] M. A. Hammami, Global stabilization of a certain class of dynamical systems using state detection, Appl. Math. Lett., vol. 14, no. 8, pp. 913–919 (Nov. 2001), doi: 10.1016/S0893-9659(01)00065-9.
[27] H. Ye, A. N. Michel, and K. Wang, Qualitative analysis of Cohen-Grossberg neural networks with multiple delays, Phys. Rev. E, vol. 51, no. 3, pp. 2611–2618 (Mar. 1995), doi: 10.1103/PhysRevE.51.2611.
[28] L. Wang and X. Zou, Exponential stability of Cohen-Grossberg neural networks, Neural Netw., vol. 15, no. 3, pp. 415–422 (Apr. 2002), doi: 10.1016/S0893-6080(02)00025-4.
[29] X. F. Liao, C. Li, and K. W. Wong, Criteria for exponential stability of Cohen-Grossberg neural networks, Neural Netw., vol. 17, no. 10, pp. 1401–1414 (Dec. 2004), doi: 10.1016/j.neunet.2004.08.007.
[30] T. Chen and L. Rong, Delay-independent stability analysis of Cohen–Grossberg neural networks, Phys. Lett. A, vol. 317, no. 5-6, pp. 436–449 (Dec. 2003), doi: 10.1016/j.physleta.2003.08.066.
[31] T. Chen and L. Rong, Robust global exponential stability of Cohen–Grossberg neural networks with time delays, IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 203–206 (Jan. 2004), doi: 10.1109/TNN.2003.822974.
[32] M. Jiang, Y. Shen, and X. Liao, Boundedness and global exponential stability for generalized Cohen–Grossberg neural networks with variable delay, Appl. Math. Comput., vol. 172, no. 1, pp. 379–393 (Jan. 2006), doi: 10.1016/j.amc.2005.02.009.
[33] N. Ozcan, New conditions for global stability of neutral-type delayed Cohen-Grossberg neural networks, Neural Netw., vol. 106, pp. 1–7 (Oct. 2018), doi: 10.1016/j.neunet.2018.06.009.
[34] R. Samli, S. Senan, E. Yucel, and Z. Orman, Some generalized global stability criteria for delayed Cohen–Grossberg neural networks of neutral-type, Neural Netw., vol. 116, pp. 198–207 (Aug. 2019), doi: 10.1016/j.neunet.2019.04.023.
[35] G. Stamov, E. Gospodinova, and I. Stamova, Practical exponential stability with respect to h-manifolds of discontinuous delayed Cohen–Grossberg neural networks with variable impulsive perturbations, Math. Model. Control, vol. 1, no. 1, pp. 26–34 (2021), doi: 10.3934/mmc.2021003.
[36] M. Benjemaa, W. Gouadri, and M. A. Hammami, New results on the uniform exponential stability of nonautonomous perturbed dynamical systems, Int. J. Robust Nonlinear Control, vol. 31, no. 12, pp. 5563–5579 (Aug. 2021), doi: 10.1002/rnc.5550.
[37] V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Dordrecht, The Netherlands: Kluwer Academic (1999), doi: 10.1007/978-94-017-1965-0.
