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Synchronization of Inertial Cohen-Grossberg-type Neural Networks with Reaction-diffusion Terms

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Abstract

This paper investigates the synchronization of inertial reaction-diffusion Cohen-Grossberg-type neural networks. Compared with the existing works concerning reaction-diffusion neural networks, the main innovation of this paper is that two design strategies of feedback synchronization controllers are proposed based on the types of time delays. For the systems with bounded differentiable delays, the sufficient conditions for synchronization are derived under the framework of Lyapunov method. If the time delay of the addressed system is unbounded or non-differentiable, it can also realize synchronization by employing the method of variation of parameters and some analytical techniques. Moreover, the proposed methods are applicable to various boundary conditions. The correctness of the obtained criteria is verified by three numerical examples.

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References

  1. J. Cao, G. Stamov, I. Stamova, and S. Simeonov, “Almost periodicity in impulsive fractional-order reaction-diffusion neural networks with time-varying delays,” IEEE Transactions on Cybernetics, vol. 51, no. 1, pp. 151–161, 2021.

    Article  Google Scholar 

  2. H. Wang, G. Wei, S. Wen, and T. Huang, “Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks,” Applied Mathematics and Computation, vol. 390, p. 125680, February 2021.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Ding, Z. Wang, and N. Rong, “Intermittent control for quasisynchronization of delayed discrete-time neural networks,” IEEE Transactions on Cybernetics, vol. 51, no. 2, pp. 862–873, February 2021.

    Article  Google Scholar 

  4. H. Que, M. Fang, G. Wu, H. Su, T. Huang, and D. Zhang, “Exponential synchronization via aperiodic sampling of complex delayed networks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 7, pp. 1399–1407, July 2019.

    Article  Google Scholar 

  5. Y. Tian and Z. Wang, “A new result on H∞ performance state estimation for static neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 388, p. 125556, January 2021.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. A. Cohen and S. Grossberg, “Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,” IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-13, no. 5, pp. 815–826, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Du and J. Lu, “New results on finite-time stability of fractional-order Cohen-Grossberg neural networks with time delays,” Asian Journal of Control, vol. 24, no. 5, pp. 2328–2337, 2022.

    Article  MathSciNet  Google Scholar 

  8. X.-Z. Liu, K.-N. Wu, X. Ding, and W. Zhang, “Boundary stabilization of stochastic delayed Cohen-Grossberg neural networks with diffusion terms,” IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 8, pp. 3227–3237, 2022.

    Article  MathSciNet  Google Scholar 

  9. F. Zhang and Z. Zeng, “Multiple ψ-type stability of Cohen-Grossberg neural networks with both time-varying discrete delays and distributed delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 2, pp. 566–579, February 2019.

    Article  MathSciNet  Google Scholar 

  10. R. Li and J. Cao, “Exponential stabilization of inertial quaternion-valued Cohen-Grossberg neural networks: Lexicographical order method,” International Journal of Robust and Nonlinear Control, vol. 30, no. 13, pp. 5205–5220, September 2020.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Pu and F. Li, “Finite-/fixed-time synchronization for Cohen-Grossberg neural networks with discontinuous or continuous activations via periodically switching control,” Cognitive Neurodynamics, vol. 16, pp. 195–213, 2022.

    Article  Google Scholar 

  12. D. Peng, J. Li, W. Xu, and X. Li, “Finite-time synchronization of coupled Cohen-Grossberg neural networks with mixed time delays,” Journal of the Franklin Institute, vol. 357, no. 16, pp. 11349–11367, November 2020.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Chen, Y. Huang, and S. Ren, “Passivity and robust passivity of delayed Cohen-Grossberg neural networks with and without reaction-diffusion terms,” Circuits, Systems, and Signal Processing, vol. 37, no. 7, pp. 2772–2804, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. Lu, “Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions,” Chaos, Solitons and Fractals, vol. 35, no. 1, pp. 116–125, January 2008.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Wang, H. Wu, T. Huang, S. Ren, and J. Wu, “Passivity analysis of coupled reaction-diffusion neural networks with Dirichlet boundary conditions,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2148–2159, August 2017.

    Article  Google Scholar 

  16. S. Lin, J. Wang, X. Chen, K. Shi, and H. Shen, “H∞ fuzzy state estimation for delayed genetic regulatory networks with random gain fluctuations and reaction-diffusion,” Journal of the Franklin Institute, vol. 358, no. 16, pp. 8694–8714, October 2021.

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Zhang and Z. Zeng, “Stability and synchronization of nonautonomous reaction-diffusion neural networks with general time-varying delays,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–14, April 2021. DOI: https://doi.org/10.1109/TNNLS.2021.3071404

  18. R. Li, J. Cao, A. Alsaedi, and F. Alsaadi, “Exponential and fixed-time synchronization of Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms,” Applied Mathematics and Computation, vol. 313, pp. 37–51, November 2017.

    Article  MathSciNet  MATH  Google Scholar 

  19. X. Li, X. Song, Z. Ning, and J. Lu, “Quasi-synchronization of hybrid coupled reaction-diffusion neural networks with parameter mismatches via time-space sampled-data control,” International Journal of Control, Automation, and Systems, vol. 19, no. 9, pp. 3087–3100, September 2021.

    Article  Google Scholar 

  20. X. Song, R. Zhang, M. Wang, and J. Lu, “Nonfragile dissipative synchronization of reaction-diffusion complex dynamical networks with coupling delays,” International Journal of Control, Automation, and Systems, vol. 19, no. 3, pp. 1252–1263, March 2021.

    Article  Google Scholar 

  21. C. Fu and A. Wu, “Global exponential stability of reaction-diffusion delayed BAM neural networks with Dirichlet boundary condition,” Proc. of International Symposium on Neural Networks, vol. 5551, pp. 303–312, 2009.

    Google Scholar 

  22. Y. Ke and C. Miao, “Stability analysis of inertial Cohen-Grossberg-type neural networks with time delays,” Neurocomputing, vol. 117, pp. 196–205, October 2013.

    Article  Google Scholar 

  23. X. Song, J. Man, C. K. Ahn, and S. Song, “Finite-time dissipative synchronization for Markovian jump generalized inertial neural networks with reaction-diffusion terms,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 6, pp. 3650–3661, June 2021.

    Article  Google Scholar 

  24. R. Guo, J. Lu, Y. Li, and W. Lv, “Fixed-time synchronization of inertial complex-valued neural networks with time delays,” Nonlinear Dynamics, vol. 105, pp. 1643–1656, 2021.

    Article  Google Scholar 

  25. X. Wei, Z. Zhang, C. Lin, and J. Chen, “Synchronization and anti-synchronization for complex-valued inertial neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 403, no. 126194, 2021.

  26. P. Wan, D. Sun, D. Chen, M. Zhao, and L. Zheng, “Exponential synchronization of inertial reaction-diffusion coupled neural networks with proportional delay via periodically intermittent control,” Neurocomputing, vol. 356, pp. 195–205, 2019.

    Article  Google Scholar 

  27. S. Dharano, R. Rakkiyappan, and J. Park, “Pinning sampled-data synchronization of coupled inertial neural networks with reaction-diffusion terms and time-varying delays,” Neurocomputing, vol. 227, pp. 101–107, 2017.

    Article  Google Scholar 

  28. L. Sun, L. Su and J. Wang, “Non-fragile dissipative state estimation for semi-Markov jump inertial neural networks with reaction-diffusion,” Applied Mathematics and Computation, vol. 411, no. 126404, December 2021.

  29. Y. Sheng and Z. Zeng, “Synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and unbounded delays,” Neural Networks, vol. 93, pp. 89–98, September 2017.

    Article  MATH  Google Scholar 

  30. Q. Chang, Y. Yang, L. Li, and F. Wang, “The optimization of control parameters: Finite-time and fixed-time synchronization of inertial memristive neural networks with proportional delays and switching jumps mismatch,” International Journal of Control, Automation, and Systems, vol. 19, pp. 2491–2499, July 2021.

    Article  Google Scholar 

  31. T. Zhang and F. Deng, “Adaptive finite-time synchronization of stochastic mixed time-varying delayed memristor-based neural networks,” Neurocomputing, vol. 452, pp. 781–788, September 2021.

    Article  Google Scholar 

  32. X. Zhang, P. Niu, N. Liu, and G. Li, “Global synchronization in finite-time of fractional-order complexvalued delayed Hopfield neural networks,” International Journal of Control, Automation, and Systems, vol. 17, pp. 521–535, February 2021.

    Article  Google Scholar 

  33. Y. Liu, Z. Wang, J. Liang, and X. Liu, “Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays,” IEEE Transactions on Cybernetics, vol. 43, pp. 102–114, February 2013.

    Article  Google Scholar 

  34. Q. Gan, T. Lv, and Z. Fu, “Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control,” Chaos, vol. 26, no. 043113, 2016.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Mingchen Huan & Chuandong Li

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  1. Mingchen Huan
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  2. Chuandong Li
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Correspondence to Chuandong Li.

Additional information

Mingchen Huan received his B.S. degree from the College of Computer and Information Science, Southwest University, Chongqing, China, in June 2020, and he is studying for an M.S. degree in signal and information processing at the College of Electronic and Information Engineering, Southwest University, Chongqing, China. His current research interests include stability theory of neural networks and impulsive dynamical systems.

Chuandong Li received his B.S. degree in applied mathematics from Sichuan University, Chengdu, China in 1992, and an M.S. degree in operational research and control theory, and a Ph.D. degree in computer software and theory from Chongqing University, Chongqing, China, in 2001 and 2005, respectively. He has been a Professor at the College of Electronic and Information Engineering, Southwest University, Chongqing, China, since 2012, and has been an IEEE Senior member since 2010. From November 2006 to November 2008, he served as a research fellow in the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China. He has published more than 200 journal papers. His current research interests include computational intelligence, neural networks, memristive systems, chaos control and synchronization, and impulsive dynamical systems.

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This work is supported by National Key Research and Development Project (Grant No. 2018AAA0100101).

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Huan, M., Li, C. Synchronization of Inertial Cohen-Grossberg-type Neural Networks with Reaction-diffusion Terms. Int. J. Control Autom. Syst. 20, 4059–4075 (2022). https://doi.org/10.1007/s12555-021-0721-9

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  • DOI: https://doi.org/10.1007/s12555-021-0721-9

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