随机多组模型的平稳分布

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随机多组模型的平稳分布
Stationary Distribution Analysis for Stochastic Multi-Group Models

DOI: 10.12677/AAM.2021.101001, PDF, 下载: 655 浏览: 839 科研立项经费支持
作者: 袁俊叶, 张一帆, 郭英：青岛理工大学理学院，山东青岛
关键词: 平稳分布；图论；随机多组模型；随机耦合振子；Stationary Distribution； Graph Theory； Stochastic Multi-Group Models； Stochastic Coupled Oscillators

摘要: 本文主要利用图论的方法分析具有扩散的随机多组模型的平稳分布。然后，我们利用Lyapunov方法和图论得到了两＾保证平稳分布存在的主要定理，其中得到的充分条件具有较少的保守性，反映了平稳分布与随机扰动和拓扑结构密切相关。此外，理论结果被应用到随机耦合振子中。最后，通过数值模拟说明了本文结果的有效性。

Abstract: This paper mainly uses graph theory to analyze the stationary distribution for stochas- tic multi-group models with dispersal. Two main theorems are obtained to guarantee the existence of a stationary distribution via Lyapunov method and graph theory, in which sufficient conditions derived are less conservative and they reflect that station- ary distribution having a close connection with stochastic disturbance and topological structure. Furthermore, theoretical results are used to analyze tochastic coupled os- cillators. In the end, numerical simulation is given to demonstrate the availability of our results.

文章引用：袁俊叶, 张一帆, 郭英. 随机多组模型的平稳分布[J]. 应用数学进展, 2021, 10(1): 1-15. https://doi.org/10.12677/AAM.2021.101001

参考文献

[1]	Lajmanovich, A. and Yorke, J.A. (1976) A Deterministic Model for Gonorrhea in a Nonhomo- geneous Population. Mathematical Biosciences, 28, 221-236. https://doi.org/10.1016/0025-5564(76)90125-5
[2]	Huang, W. and Castillo-Chavez, C.C. (1992) Stability and Bifurcation for a Multiple-Group Model for the Dynamics of HIV/AIDS Transmission. Siam Journal on Applied Mathematics, 52, 835-854. https://doi.org/10.1137/0152047
[3]	Iggidr, A., Sallet, G. and Souza, M.O. (2016) On the Dynamics of a Class of Multi-Group Models for Vector-Borne Diseases. Journal of Mathematical Analysis and Applications, 441, 723-743. https://doi.org/10.1016/j.jmaa.2016.04.003
[4]	Zhang, C.M., Li, W.X. and Wang, K.E. (2015) Graph-Theoretic Approach to Stability of Multi-Group Models with Dispersal. Discrete and Continuous Dynamical Systems, Series B, 20, 259-280.
[5]	Li, M.Y. and Zhi, S. (2010) Global-Stability Problem for Coupled Systems of Differential Equations on Networks. Journal of Differential Equations, 248, 1-20. https://doi.org/10.1016/j.jde.2009.09.003
[6]	Toutonji, O., Yoo, S. and Park, M. (2012) Stability Analysis of VEISV Propagation Modeling for Network Worm Attack. Applied Mathematical Modelling, 36, 2751-2761. https://doi.org/10.1016/j.apm.2011.09.058
[7]	Gong, Y.W., Song, Y.R. and Jiang, G.P. (2013) Global Dynamics of a Novel Multi-Group Model for Computer Worms. Chinese Physics B, 22, 56-62. https://doi.org/10.1088/1674-1056/22/4/040204
[8]	Li, W.X., Zhang, X.Q. and Zhang, C.M. (2015) Exponential Stability of Delayed Multi-Group Model with Reaction-Diffusion and Multiple Dispersal Based on Razumikhin Technique and
[9]	Graph Theory. Communications in Nonlinear Science and Numerical Simulation, 27, 237-253. https://doi.org/10.1016/j.cnsns.2015.03.012
[10]	Guo, H., Li, M.Y. and Shuai, Z. (2006) Global Stability of the Endemic Equilibrium of Multi- group SIR Epidemic Models. Canadian Applied Mathematics Quarterly, 14, 259-284.
[11]	Liu, Z.J., Hu, J. and Wang, L.W. (2017) Modelling and Analysis of Global Resurgence of Mumps: A Multi-Group Epidemic Model with Asymptomatic Infection, General Vaccinated and Exposed Distributions. Nonlinear Analysis: Real World Application, 37, 137-161. https://doi.org/10.1016/j.nonrwa.2017.02.009
[12]	Guo, Y., Zhao, W. and Ding, X.H. (2019) Input-to-State Stability for Stochastic Multi-Group Models with Multi-Dispersal and Time-Varying Delay. Applied Mathematics and Computation, 343, 114-127. https://doi.org/10.1016/j.amc.2018.07.058
[13]	Wang, Z.G., Fan, X.M. and Han, Q.X. (2013) Global Stability of Deterministic and Stochastic Multigroup SEIQR Models in Computer Network. Applied Mathematics Modeling, 37, 8673- 8686. https://doi.org/10.1016/j.apm.2013.07.037
[14]	Xue, Y.K., Yuan, X.P. and Liu, M.X. (2014) Global Stability of a Multi-Group SEI Model. Applied Mathematics and Computation, 226, 51-60. https://doi.org/10.1016/j.amc.2013.09.050
[15]	Zou, X.L., Fan, D.J. and Wang, K. (2013) Stationary Distribution and Stochastic Hopf Bi- furcation for a Predator-Prey System with Noises. Discrete Continuous Dynamical Systems, Series B, 18, 1507-1519. https://doi.org/10.3934/dcdsb.2013.18.1507
[16]	Yin, F.C. and Yu, X.Y. (2015) The Stationary Distribution and Extinction of Generalized Multispecies Stochastic Lotka-Volterra Predator-Prey System. Mathematical Problems in En- gineering, 2015, Article ID: 479326. https://doi.org/10.1155/2015/479326
[17]	Zhao, Y., Yuan, S.L. and Ma, J.L. (2015) Survival and Stationary Distribution Analysis of a Stochastic Competitive Model of Three Species in a Polluted Environment. Bulletin of Math- ematical Biology, 77, 1285-1326. https://doi.org/10.1007/s11538-015-0086-4
[18]	Dang, N.H., Du, N.H. and Guo, Y. (2014) Existence of Stationary Distributions for Kolmogorov Systems of Competitive Type under Telegraph Noise. Journal of Differential Equations, 257, 2078-2101. https://doi.org/10.1016/j.jde.2014.05.029
[19]	Zhou, Y.L., Zhang, W.G. and Yuan, S.L. (2014) Survival and Stationary Distribution of a SIR Epidemic Model with Stochastic Perturbations. Applied Mathematics and Computation, 244, 118-131. https://doi.org/10.1016/j.amc.2014.06.100
[20]	Zhou, Y., Zhang, W. and Yuan, S. (2013) Survival and Stationary Distribution in a Stochastic SIS Model. Discrete Dynamics in Nature and Society, 2013, Article ID: 172726. https://doi.org/10.1155/2013/172726
[21]	Mao, X.R. (2011) Stationary Distribution of Stochastic Population Systems. Systems and Control Letters, 60, 398-405. https://doi.org/10.1016/j.sysconle.2011.02.013
[22]	Liu, M. and Wang, K. (2012) Stationary Distribution, Ergodicity and Extinction of a Stochastic Generalized Logistic System. Applied Mathematics Letters, 25, 1980-1985. https://doi.org/10.1016/j.aml.2012.03.015
[23]	Mao, X.R., Yuan, C. and Guo, Y. (2005) Numerical Method for Stationary Distribution of Stochastic Differential Equations with Markovian Switching. Journal of Computational and Applied Mathematics, 174, 1-27. https://doi.org/10.1016/j.cam.2004.03.016
[24]	Hasminskii, R.Z. (1969) Stochastic Stability of Differential Equations. Sijthoff & Noordhoff.
[25]	Huang, W., Ji, M., Liu, Z. and Yi, Y. (2015) Steady States of Fokker-Planck Equations: I. Existence. Journal of Dynamics and Differential Equation, 27, 721-742. https://doi.org/10.1007/s10884-015-9454-x
[26]	Mao, X.R. (1997) Stochastic Differential Equations and Applications. Horwood, Chichester.
[27]	Zhu, C. and Guo, Y. (2007) Asymptotic Properties of Hybrid Diffusion Systems. SIAM Journal on Control and Optimization, 46, 1151-1179. https://doi.org/10.1137/060649343
[28]	Zhang, C.M. and Han, B.S. (2020) Stability Analysis of Stochastic Delayed Complex Networks with Multi-Weights Based on Razumikhin Technique and Graph Theory. Physica A: Statistical Mechanics and Its Applications, 538, Article ID: 122827. https://doi.org/10.1016/j.physa.2019.122827
[29]	Wang, J.W., Feng, C., Xu, M.Z. and Chen, Y. (2016) The Synchronization of Instantaneously Coupled Harmonic Oscillators Using Sampled Data with Measurement Noise. Automatica, 66, 155-162. https://doi.org/10.1016/j.automatica.2016.01.012
[30]	Wu, Y., Cao, J., Li, Q., Alsaedi, A. and Alsaadi, F.E. (2017) Finite-Time Synchronization of Uncertain Coupled Switched Neural Networks under Asynchronous Switching. Neural Net- works, 85, 128-139. https://doi.org/10.1016/j.neunet.2016.10.007

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