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The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps

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  • Rathinasamy, Anandaraman
  • Mayavel, Pichamuthu

Abstract

The balanced numerical approximations of the stochastic neutral Hopfield neural networks (SNHNN) with time delay and Poisson jumps are examined to ascertain the nature of the mathematical model. The numerical approximations of the balanced split-step theta methods for the SNHNN with time delay and Poisson jumps are taken into consideration primarily because they maintain almost surely (a.s.) exponential stability property of numerical methods and produce negligible mean square error when compared to other approaches. Furthermore, in the recent development of numerical approximations for SNHNN with time delay, we note that balanced split-step theta-approximations are a more stable scheme. We showed that the numerical approximations of balanced split-step theta methods of SNHNN with time delay and Poisson jumps have strong convergence order 1/2 and are numerically almost exponentially stable by applying some theoretical significance criteria.Moreover, our main research tools are Lipschitz conditions, linear growth conditions, and the discrete semi martingale convergence theorem. Through numerical experiments, we try to demonstrate the theoretical results obtained in this paper. Finally, we got the confirmation about the theoretical results of the split-step theta-approximations of SNHNN with time delay and Poisson jumps via particular numerical example.

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  • Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    • Handle: RePEc:eee:apmaco:v:455:y:2023:i:c:s0096300323002989
    DOI: 10.1016/j.amc.2023.128129
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    References listed on IDEAS

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    1. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Liu, Linna & Zhu, Quanxin, 2015. "Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 698-712.
    3. Huabin Chen & Yang Zhao, 2015. "Delay-dependent exponential stability for uncertain neutral stochastic neural networks with interval time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(14), pages 2584-2597, October.
    4. Qian Guo & Wenwen Xie & Taketomo Mitsui, 2013. "Convergence and Stability of the Split-Step -Milstein Method for Stochastic Delay Hopfield Neural Networks," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, April.
    5. Lou, Xuyang & Cui, Baotong, 2009. "Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2188-2197.
    6. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    7. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    8. Rathinasamy, A. & Narayanasamy, J., 2019. "Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 126-152.
    9. Tan, Jianguo & Tan, Yahua & Guo, Yongfeng & Feng, Jianfeng, 2020. "Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    10. Ma, Li & Li, Yujing & Zhu, Quanxin, 2023. "Stability analysis for a class of stochastic delay nonlinear systems driven by G-Lévy Process," Statistics & Probability Letters, Elsevier, vol. 195(C).
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