Global exponential stability for generalized Cohen-Grossberg neural networks with variable delay
*Wided GouadriCorresponding authorgouadri2016@gmail.comDepartment of Mathematics Laboratory Stability and Control of Systems and nonlinear PDEs Faculty of Sciences of Sfax University of SfaxBP 1171, Rte Soukra Sfax, 3000, Tunisia0009-0008-3049-1249View full profile → , Mohamed Ali Hammamimohamedali.hammami@fss.rnu.tnDepartment of Mathematics Laboratory Stability and Control of Systems and nonlinear PDEs Faculty of Sciences of Sfax University of SfaxDepartment of Mathematics Faculty of Sciences of Sfax University of SfaxSfax, Sfax, 3029, Tunisia0000-0002-9347-4525View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 Apr 2025
- Published Online:
- 22 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2338
- Pages:
- 875–890
Abstract
Keywords
Subject Classifications
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.




