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 引用本文: 王春生. 中立多变时滞Volterra型随机动力系统的稳定性 [J]. 应用数学和力学，2021，42（11）：1190-1202
WANG Chunsheng. Stability of Neutral Volterra Stochastic Dynamical Systems With Multiple Delays[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1190-1202. doi: 10.21656/1000-0887.410323
 Citation: WANG Chunsheng. Stability of Neutral Volterra Stochastic Dynamical Systems With Multiple Delays[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1190-1202.

中立多变时滞Volterra型随机动力系统的稳定性

doi: 10.21656/1000-0887.410323

作者简介:王春生（1982—），男，副教授，硕士（E-mail： paperspring@163.com）
• 中图分类号: O231.3

Stability of Neutral Volterra Stochastic Dynamical Systems With Multiple Delays

• 摘要: 探讨了一类非线性随机积分微分动力系统，并通过Banach不动点方法，给出了该系统零解均方渐近稳定的充要条件，形成了中立多变时滞Volterra型随机积分微分动力系统零解均方渐近稳定性定理。与前人的研究方法不同，该文根据多变时滞随机动力系统各时滞的特点，灵活构造算子，相比以往文献的方法更加灵活实用。文章的结论一定程度上改进和发展了相关研究论文的结果。另外，文章所得结论补充并推广了不动点方法在研究非线性中立多变时滞Volterra型随机积分微分动力系统零解稳定性方面的成果。
•  [1] 李岩汀, 许锡宾, 周世良, 等. 基于径向基函数逼近的非线性动力系统数值求解[J]. 应用数学和力学, 2016, 37(3): 311-318. (LI Yanting, XU Xibin, ZHOU Shiliang, et al. A numerical approximation method for nonlinear dynamic systems based on radial basis functions[J]. Applied Mathematics and Mechanics, 2016, 37(3): 311-318.(in Chinese) [2] BURTON T A. Fixed points and differential equations with asymptotically constant or periodic solution[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2004, 11: 1-31. [3] BURTON T A. Fixed points and stability of a nonconvolution equation[J]. Proceedings of the American Mathematical Society, 2004, 132: 3679-3687. [4] ZHANG B. Fixed points and stability in differential equations with variable delays[J]. Nonlinear Analysis: Theory Methods & Applications, 2005, 63(5/7): e233-e242. [5] BURTON T A. Fixed points, stability, and exact linearization[J]. Nonlinear Analysis: Theory Methods & Applications, 2005, 61: 857-870. [6] BURTON T A, FURUMOCHI T. Krasnoselskii’s fixed point theorem and stability[J]. Nonlinear Analysis: Theory Methods & Applications, 2002, 49(4): 445-454. [7] BURTON T A, ZHANG B. Fixed points and stability of an integral equation: nonuniqueness[J]. Applied Mathematics Letters, 2004, 17(7): 839-846. [8] FURUMOCHI T. Stabilities in FDEs by Schauder’s theorem[J]. Nonlinear Analysis: Theory, Methods & Applications, 2005, 63(5/7): e217-e224. [9] RAFFOUL Y N. Stability in neutral nonlinear differential equations with functional delays using fixed-point theory[J]. Mathematical and Computer Modelling, 2004, 40(7/8): 691-700. [10] LUO J W. Fixed points and stability of neutral stochastic delay differential equations[J]. Journal of Mathematical Analysis and Applications, 2007, 334(1): 431-440. [11] 王春生, 李永明. 中立型多变时滞随机微分方程的稳定性[J]. 山东大学学报(理学版), 2015, 50(5): 82-87. (WANG Chunsheng, LI Yongming. Stability of neutral stochastic differential equations with some variable delays[J]. Journal of Shandong University (Natural Science), 2015, 50(5): 82-87.(in Chinese) [12] 王春生, 李永明. 三类不动点与一类随机动力系统的稳定性[J]. 控制理论与应用, 2017, 34(5): 677-682. (WANG Chunsheng, LI Yongming. Three kinds of fixed points and stability of stochastic dynamical systems[J]. Control Theory and Applications, 2017, 34(5): 677-682.(in Chinese) [13] 王春生, 李永明. Krasnoselskii不动点与中立型多变时滞随机动力系统的指数p稳定性[J]. 应用力学学报, 2019, 36(4): 901-905, 1000. (WANG Chunsheng, LI Yongming. Krasnoselskii fixed point and exponential p-stability of neutral stochastic dynamic systems with time-varying delays[J]. Chinese Journal of Applied Mechanics, 2019, 36(4): 901-905, 1000.(in Chinese) [14] 王春生. 中立型随机积分微分方程的稳定性[J]. 四川理工学院学报(自然科学版), 2011, 24(1): 81-84. (WANG Chunsheng. The stability of neutral stochastic integrodifferential equations[J]. Journal of Sichuan University of Science & Engineering (Natural Science Edition), 2011, 24(1): 81-84.(in Chinese) [15] 王春生. 随机微分方程稳定性的两种不动点方法的比较[J]. 四川理工学院学报(自然科学版), 2012, 25(4): 87-90. (WANG Chunsheng. Stability of stochastic differential equations: the two fixed points of comparison[J]. Journal of Sichuan University of Science & Engineering (Natural Science Edition), 2012, 25(4): 87-90.(in Chinese) [16] WU Meng, HUANG Nanjing, ZHAO Changwen. Fixed points and stability in neutural stochastic differential equations with variable delays[J]. Fixed Point Theory and Applications, 2008, 2008: 407352.

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出版历程
• 收稿日期:  2020-10-23
• 修回日期:  2021-03-30
• 网络出版日期:  2021-12-07
• 刊出日期:  2021-11-30

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