دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,433
تعداد مقالات17,642
تعداد مشاهده مقاله57,426,857
تعداد دریافت فایل اصل مقاله19,180,737
Kopperundevi, Sivarajan. (1403). Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks. سامانه مدیریت نشریات علمی, 12(1), 136-148. doi: 10.22034/cmde.2023.55861.2330
Sivarajan Kopperundevi. "Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks". سامانه مدیریت نشریات علمی, 12, 1, 1403, 136-148. doi: 10.22034/cmde.2023.55861.2330
Kopperundevi, Sivarajan. (1403). 'Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks', سامانه مدیریت نشریات علمی, 12(1), pp. 136-148. doi: 10.22034/cmde.2023.55861.2330
Kopperundevi, Sivarajan. Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks. سامانه مدیریت نشریات علمی, 1403; 12(1): 136-148. doi: 10.22034/cmde.2023.55861.2330

Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks

Computational Methods for Differential Equations
مقاله 11، دوره 12، شماره 1، فروردین 2024، صفحه 136-148    اصل مقاله (397.66 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55861.2330
نویسنده
Sivarajan Kopperundevi*
Department of Mathematics, Dr. M.G.R Educational and Research Institute(To be Deemed), Maduravoyal, Chennai-600 095, India.
چکیده
This study examines the balanced Maruyama with two step approximations of stochastic Hopfield neural networks with delay. The main aim of this paper is to discover the conditions under which the exact solutions remain stable for the balanced Maruyama with two-step approximations of stochastic delay Hopfield neural networks (SDHNN). The semi martingale theorem for convergence is used to demonstrate the almost sure exponential stability of balanced Maruyama with two-step approximations of stochastic delay Hopfield networks. Additionally, the numerical balanced Euler approximation's stability conditions are compared. Our theoretical findings are illustrated with numerical experiments.
کلیدواژه‌ها
Almost sure exponential stability؛ Balanced two step Maruyama numerical approximations؛ Hopfield neural networks؛ Stochastic delay differential equations
مراجع
  • [1] S. Blythe, X. Mao, and X. Liao, Stability of stochastic delay neural networks, J. Franklin Inst., 338 (2001), 481-495.
  • [2] E. Buckwar and R. Winkler, Multi-step Maruyama methods for stochastic delay differential equations,  Stoch.  Anal. Appl., 25 (2007), 933-959.
  • [3] W. Cao and Z. Zhang, On exponential mean-square stability of two-step Maruyama methods for stochastic delay differential equations, J. Comput. Appl. Math., 245 (2013), 182-193.
  • [4] D. J. Higham, X. Mao, and C. Yuan, Almost sure  and moment exponential stability in the numerical simulation    of stochastic differential equations, SIAM J. Numer. Anal., 45 (2007), 592-609.
  • [5] C. Huang, P. Chen, Y. He, L. Huang, and W. Tan, Almost sure exponential stability of delayed Hopfield neural networks, Appl. Math. Lett., 21 (2008), 701-705.
  • [6] X. Li and W. Cao, On mean-square stability of two-step Maruyama methods for nonlinear neutral stochastic delay differential equations, Appl. Math. Comput., 261 (2015), 373-381.
  • [7] L. Liu and Q. Zhu, Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks, Appl. Math. Comput., 266 (2015), 698-712.
  • [8] X. Mao, Stochastic differential equations and applications, Harwood, Chichester 1997.
  • [9] A. Rathinasamy and P. Mayavel, Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks. Appl. Math. Comput., 438 (2023), 127573.
  • [10] A. Rathinasamy and J. Narayanasamy, Mean square stability and almost sure exponential stability of two-step Maruyama methods of stochastic delay Hopfield neural networks, Appl. Math. Comput., 348 (2019), 126-152.
  • [11] L. Ronghua, W. K. Pang, and P. K. Leung, Exponential stability of numerical solutions to stochastic delay Hopfield neural networks, Neurocomputing, 73 (2010), 920-926.
  • [12] J. Tan, P. Mayavel, A. Rathinasamy, and H. Cao, A new convergence and positivity analysis of balanced Euler method for stochastic age-dependent population equations, Numer. Methods Partial Differ. Equ., 37 (2) (2021), 1752-1765.
  • [13] L. Wan and J. Sun, Mean  square exponential stability of stochastic delayed Hopfield neural networks, Phys. Lett.  A, 343 (2005), 306-318.
  • [14] Q. Zhou and L. Wan, Exponential stability of stochastic delayed Hopfield neural networks, Appl. Math. Comput., 199 (2008), 84-89.
آمار
تعداد مشاهده مقاله: 325
تعداد دریافت فایل اصل مقاله: 707


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب