2607004477
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The Global Exponential Stability of Neutral-Type Delayed Inertial Neural Networks

  • Wentao Wang 1,   
  • Wei Chen 2,*

Received: 11 May 2026 | Revised: 15 Jun 2026 | Accepted: 01 Jul 2026 | Published: 15 Jul 2026

Abstract

This paper presents an analysis of neutral-type delayed inertial neural networks (NDINNs) by using the characteristic method. The study introduces three novel sufficient conditions for the global exponential stability of NDINNs, formulated as a series of linear scalar inequalities. This approach sets them apart from previous results and facilitates straightforward solutions. The theoretical findings are validated through three numerical examples, each accompanied by relevant simulations.

References 

  • 1.

    Babcock, K.; Westervelt, R. Stability and dynamics of simple electronic neural networks with added inertia. Phys. D 1986, 23, 464–469.

  • 2.

    Babcock, K.; Westervelt, R. Dynamics of simple electronic neural networks. Phys. D 1987, 28, 305–316.

  • 3.

    Lakshmanana, S.; Lima, C.; Prakashb, M.; et al. Neutral-type of delayed inertial neural networks and their stability analysis using the LMI approach. Neurocomputing 2017, 230, 243–250.

  • 4.

    Duan, L.; Jiana, J.; Wang, B. Global exponential dissipativity of neutral-type BAM inertial neural networks with mixed time-varying delays. Neurocomputing 2020, 378, 399–412.

  • 5.

    Zhou, F.; Yao, H. Stability analysis for neutral-type inertial BAM neural networks with time-varying delays. Nonlinear Dyn. 2018, 92, 1583–1598.

  • 6.

    Tu, Z.; Cao, J.; Alsaedi, A.; et al. Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw. 2017, 88, 125–133.

  • 7.

    Duan, L.; Li, J. Fixed-time synchronization of fuzzy neutral-type BAM memristive inertial neural networks with proportional delays. Inf. Sci. 2021, 576, 522–541.

  • 8.

    Aouiti, C.; Hui, Q.; Jallouli, H.; et al. Fixed-time stabilization of fuzzy neutral-type inertial neural networks with time-varying delay. Fuzzy Sets Syst. 2021, 411, 48–67.

  • 9.

    Zhang, J.; Chang, A.; Yang, G. Periodicity on neutral-type inertial neural networks incorporating multiple delays. Symmetry 2021, 13, 2231.

  • 10.

    Zhou, Z.; Zhang, Z.; Chen, M. Finite-time synchronization for fuzzy delayed neutral-type inertial Bam neural networks via the figure analysis approach. Int. J. Fuzzy Syst. 2022, 24, 229–246.

  • 11.

    Ezzinbi, K.; Besseme, F. Dynamics of μ-piecewise pseudo almost periodic solutions of neutral-type inertial neural networks models: existence and attractiveness. Cogn. Neurodyn. 2022, 16, 455–469.

  • 12.

    Aouiti, C.; Assali, E.; Gharbia, I.; et al. Existence and exponential stability of piecewise pseudo almost periodic solution of neutral-type inertial neural networks with mixed delay and impulsive perturbations. Neurocomputing 2019, 357, 292–309.

  • 13.

    Jian, J.; Duan, L. Finite-time synchronization for fuzzy neutral-type inertial neural networks with time-varying coefficients and proportional delays. Fuzzy Sets Syst. 2020, 381, 51–67.

  • 14.

    Jia, S.; Zhou, L. Fixed-time stabilization of fuzzy neutral-type inertial neural networks with proportional delays. ISA Trans. 2024, 144, 167–175.

  • 15.

    Xu, M.; Du, B. Periodic solution for neutral-type inertial neural networks with time-varying delays. Adv. Differ. Equ. 2020, 2020, 607.

  • 16.

    Wu, K.; Jian, J. Non-reduced order strategies for global dissipativity of memristive neutral-type inertial neural networks with mixed time-varying delays. Neurocomputing 2021, 436, 174–183.

  • 17.

    Wang, Q.; Duan, L.; Huang, L.; et al. Global exponential stability of a periodic inertial memristive neural networks with time delays: Characteristic approach. Neurocomputing 2026, 668, 132408.

  • 18.

    Wang, W.; Chen, W. New study on neutral-type inertial BAM neural networks via the characteristic method. J. Math. Anal. Appl. 2026, 557, 130325.

  • 19.

    Fort, M.; Tesi, A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 1995, 42, 345–366.

  • 20.

    Wang, W.; Wu, J.; Chen, W. The characteristics method to study global exponential stability of delayed inertial neural networks. Math. Comput. Simul. 2025, 232, 91–101.

  • 21.

    Wang, W. Mean-square exponential input-to-state stability of stochastic delayed recurrent neural networks with local Lipschitz condition. Math. Methods Appl. Sci. 2023, 46, 17788–17797.

  • 22.

    Arif, M.S.; Raza, A.; Abodayeh, K.; et al. A Numerical Efficient Technique for the Solution of Susceptible Infected Recovered Epidemic Model. Comput. Model. Eng. Sci. 2020, 124, 477–491.

  • 23.

    Raza, A.; Awrejcewicz, J.; Rafiq, M.; et al. Stochastic analysis of nonlinear cancer disease model through virotherapy and computational methods. Mathematics 2022, 10, 368.

  • 24.

    Raza, A.; Awrejcewicz, J.; Rafiq, M.; et al. Breakdown of a nonlinear stochastic Nipah virus epidemic models through efficient numerical methods. Entropy 2021, 23, 1588.

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How to Cite
Wang, W.; Chen, W. The Global Exponential Stability of Neutral-Type Delayed Inertial Neural Networks. Complex Systems Stability & Control 2026, 2 (3), 5. https://doi.org/10.53941/cssc.2026.100016.
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