Exponential stability of Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays

Qinghua Zhou; Li Wan; Hongshan Wang; Hongbo Fu; Qunjiao Zhang; Qinghua Zhou; Li Wan; Hongshan Wang; Hongbo Fu; Qunjiao Zhang

doi:10.3934/math.2023978

AIMS Mathematics

2023, Volume 8, Issue 8: 19161-19171. doi: 10.3934/math.2023978

Previous Article Next Article

Research article

Exponential stability of Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays

1.
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
2.
Research Center of Nonlinear Science, Research Center for Applied Mathematics and Interdisciplinary Sciences, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430073, China

Received: 19 April 2023 Revised: 25 May 2023 Accepted: 29 May 2023 Published: 07 June 2023
MSC : 32D40

Maybe because Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays cannot be converted into the vector-matrix forms, the stability results of such networks are relatively few and the stability conditions in the linear matrix inequality forms have not been established. So this paper investigates the exponential stability of the networks and gives the sufficient condition in the linear matrix inequality forms. Two examples are provided to demonstrate the effectiveness of the theoretical results.
- Cohen-Grossberg neural networks,
- multiple delays,
- exponential stability
Citation: Qinghua Zhou, Li Wan, Hongshan Wang, Hongbo Fu, Qunjiao Zhang. Exponential stability of Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays[J]. AIMS Mathematics, 2023, 8(8): 19161-19171. doi: 10.3934/math.2023978

Related Papers:

Abstract

Maybe because Cohen-Grossberg neural networks with multiple time-varying delays and distributed delays cannot be converted into the vector-matrix forms, the stability results of such networks are relatively few and the stability conditions in the linear matrix inequality forms have not been established. So this paper investigates the exponential stability of the networks and gives the sufficient condition in the linear matrix inequality forms. Two examples are provided to demonstrate the effectiveness of the theoretical results.

References

[1]	M. A. Cohen, S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Syst. Man. Cy. B, 13 (1983), 815–826. https://doi.org/10.1109/TSMC.1983.6313075 doi: 10.1109/TSMC.1983.6313075
[2]	Y. Takahashi, Solving optimization problems with variable-constraint by an extended Cohen-Grossberg model, Theor. Comput. Sci., 158 (1996), 279–341. https://doi.org/10.1016/0304-3975(95)00085-2 doi: 10.1016/0304-3975(95)00085-2
[3]	J. H. Wu, Introduction to Neural Dynamics and Signal Transmission Delay, Berlin: Walter de Gruyter, 2001.
[4]	S. Gao, R. Shen, T. R. Chen, Periodic solutions for discrete-time Cohen-Grossberg neural networks with delays, Phys. Lett. A, 383 (2019), 414–420. https://doi.org/10.1016/j.physleta.2018.11.016 doi: 10.1016/j.physleta.2018.11.016
[5]	B. Sun, Y. T. Cao, Z. Y. Guo, Z. Yan, S. P. Wen, Synchronization of discrete-time recurrent neural networks with time-varying delays via quantized sliding mode control, Appl. Math. Comput., 375 (2020), 125093. https://doi.org/10.1016/j.amc.2020.125093 doi: 10.1016/j.amc.2020.125093
[6]	Y. X. Wang, Y. T. Cao, Z. Y. Guo, T. W. Huang, S. P. Wen, Event-based sliding-mode synchronization of delayed memristive neural networks via continuous/periodic sampling algorithm, Appl. Math. Comput., 383 (2020), 125379. https://doi.org/10.1016/j.amc.2020.125379 doi: 10.1016/j.amc.2020.125379
[7]	W. Q. Shen, X. Zhang, Y. T. Wang, Stability analysis of high order neural networks with proportional delays, Neurocomputing, 372 (2020), 33–39. https://doi.org/10.1016/j.neucom.2019.09.019 doi: 10.1016/j.neucom.2019.09.019
[8]	O. Faydasicok, A new Lyapunov functional for stability analysis of neutral-type Hopfield neural networks with multiple delays, Neural Networks, 129 (2020), 288–297. https://doi.org/10.1016/j.neunet.2020.06.013 doi: 10.1016/j.neunet.2020.06.013
[9]	L. Wan, Q. H. Zhou, Stability analysis of neutral-type Cohen-Grossberg neural networks with multiple time-varying delays, IEEE Access, 8 (2020), 27618–27623. https://doi.org/10.1109/ACCESS.2020.2971839 doi: 10.1109/ACCESS.2020.2971839
[10]	H. M. Wang, G. L. Wei, S. P. Wen, T. W. Huang, Generalized norm for existence, uniqueness and stability of Hopfield neural networks with discrete and distributed delays, Neural Networks, 128 (2020), 288–293. https://doi.org/10.1016/j.neunet.2020.05.014 doi: 10.1016/j.neunet.2020.05.014
[11]	Q. K. Song, Y. X. Chen, Z. J. Zhao, Y. R. Liu, F. E. Alsaadi, Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties, Neurocomputing, 420 (2021), 70–81. https://doi.org/10.1016/j.neucom.2020.08.059 doi: 10.1016/j.neucom.2020.08.059
[12]	L. Wan, Q. H. Zhou, H. B. Fu, Q. J. Zhang, Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays, AIMS Mathematics, 6 (2021), 8030–8043. https://doi.org/10.3934/math.2021466 doi: 10.3934/math.2021466
[13]	L. Wan, Q. H. Zhou, Exponential stability of neutral-type Cohen-Grossberg neural networks with multiple time-varying delays, IEEE Access, 9 (2021), 48914–48922. https://doi.org/10.1109/ACCESS.2021.3068191 doi: 10.1109/ACCESS.2021.3068191
[14]	Y. K. Deng, C. X. Huang, J. D. Cao, New results on dynamics of neutral type HCNNs with proportional delays, Math. Comput. Simul., 187 (2021), 51–59. https://doi.org/10.1016/j.matcom.2021.02.001 doi: 10.1016/j.matcom.2021.02.001
[15]	Z. J. Zhang, X. Zhang, T. T. Yu, Global exponential stability of neutral-type Cohen-Grossberg neural networks with multiple time-varying neutral and discrete delays, Neurocomputing, 490 (2022), 124–131. https://doi.org/10.1016/j.neucom.2022.03.068 doi: 10.1016/j.neucom.2022.03.068
[16]	R. V. Aravind, P. Balasubramaniam, Stability criteria for memristor-based delayed fractional-order Cohen-Grossberg neural networks with uncertainties, J. Comput. Appl. Math., 420 (2023), 114764. https://doi.org/10.1016/j.cam.2022.114764 doi: 10.1016/j.cam.2022.114764
[17]	L. H. Huang, C. X. Huang, B. W. Liu, Dynamics of a class of cellular neural networks with time-varying delays, Phys. Lett. A, 345 (2005), 330–344. https://doi.org/10.1016/j.physleta.2005.07.039 doi: 10.1016/j.physleta.2005.07.039
[18]	H. Y. Zhao, Global exponential stability and periodicity of cellular neural networks with variable delays, Phys. Lett. A, 336 (2005), 331–341. https://doi.org/10.1016/j.physleta.2004.12.001 doi: 10.1016/j.physleta.2004.12.001

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)