Stability of Neutral Volterra Stochastic Dynamical Systems With Multiple Delays
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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。
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关键词:
- Banach不动点 /
- 非线性 /
- 均方渐近稳定性 /
- 多变时滞 /
- 中立Volterra型随机积分微分动力系统
Abstract: A class of nonlinear stochastic integro-differential dynamical systems were discussed, the necessary and sufficient conditions for the mean-square asymptotic stability of the zero solution to the system were given by means of the Banach fixed point method, and a mean-square asymptotic stability theorem for neutral Volterra stochastic integro-differential dynamical systems with multiple delays was established. Unlike the previous research methods, according to the characteristics of each time delay of the stochastic dynamical system with multiple time delays, the operators were constructed through introduction of the corresponding functions, and then the stability of the system was studied with the Banach fixed point method. The conclusion improves and develops the results of several related research papers to a certain extent. In addition, the results obtained supplement and extend those of the fixed point method in study of the stability of zero solutions to nonlinear neutral variable-delay Volterra stochastic integro-differential dynamical systems. -
[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) doi: 10.3879/j.issn.1000-0887.2016.03.009 [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. doi: 10.1090/S0002-9939-04-07497-0 [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. doi: 10.1016/j.na.2005.02.081 [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. doi: 10.1016/S0362-546X(01)00111-0 [7] BURTON T A, ZHANG B. Fixed points and stability of an integral equation: nonuniqueness[J]. Applied Mathematics Letters, 2004, 17(7): 839-846. doi: 10.1016/j.aml.2004.06.015 [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. doi: 10.1016/j.mcm.2004.10.001 [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. doi: 10.1016/j.jmaa.2006.12.058 [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) doi: 10.7641/CTA.2017.60240 [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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