IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v119y2019icp188-195.html
   My bibliography  Save this article

Stationary distribution of stochastic Markov jump coupled systems based on graph theory

Author

Listed:
  • Liu, Yan
  • Yu, Pinrui
  • Chu, Dianhui
  • Su, Huan

Abstract

This paper focuses on the existence of a stationary distribution of stochastic Markov jump coupled systems (SMJCSs) for the first time, in which the coupling effect is considered. A new technique that is combining the graph theory, M-matrix method with the Lyapunov method is used to study stationary distribution, and sufficient conditions are presented to ensure the existence of a stationary distribution, which are more applicable and suitable for various fields, such as neural networks, biomathematics, physics and so forth. Moreover, sufficient conditions presented indicate that the existing region of stationary distribution is related to stochastic disturbance and the dimension of a system closely. Also, theoretical results are applied to stochastic Markov jump coupled oscillators systems in physics and then a specific theorem is presented. Eventually, some simulations are given to verify the feasibility and availability of our theoretical results.

Suggested Citation

  • Liu, Yan & Yu, Pinrui & Chu, Dianhui & Su, Huan, 2019. "Stationary distribution of stochastic Markov jump coupled systems based on graph theory," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 188-195.
    • Handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:188-195
    DOI: 10.1016/j.chaos.2019.01.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918302777
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.01.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    2. Feng, Jianwen & Yang, Pan & Zhao, Yi, 2016. "Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 52-68.
    3. Guo, Wenjuan & Cai, Yongli & Zhang, Qimin & Wang, Weiming, 2018. "Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2220-2236.
    4. Yongbao Wu & Wenxue Li & Jiqiang Feng, 2017. "Stabilisation of stochastic coupled systems via feedback control based on discrete-time state observations," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2850-2859, October.
    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. Ye, Zhiyong & Zhang, He & Zhang, Hongyu & Zhang, Hua & Lu, Guichen, 2015. "Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 156-165.
    7. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Jin & Guo, Ying & Liu, Xiaotong & Zhang, Yifan, 2024. "Stabilization of highly nonlinear stochastic coupled systems with Markovian switching under discrete-time state observations control," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Rui Kang & Shang Gao, 2022. "Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control," Mathematics, MDPI, vol. 10(18), pages 1-9, September.
    3. Shen, Zhihao & Zhang, Liang & Niu, Ben & Zhao, Ning, 2023. "Event-based reachable set synthesis for delayed nonlinear semi-Markov systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Bo, 2018. "A stochastic Feline immunodeficiency virus model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 448-458.
    2. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    3. Guo, Wanying & Meng, Shuyu & Qi, Ruotong & Li, Wenxue & Wu, Yongbao, 2024. "Existence of stationary distribution for stochastic coupled nonlinear strict-feedback systems with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    4. Xu, Yao & Chu, Chenyin & Li, Wenxue, 2018. "Quantized feedback control scheme on coupled systems with time delay and distributed delay: A finite-time inner synchronization analysis," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 315-328.
    5. Liu, Yan & Zhang, Di & Su, Huan & Feng, Jiqiang, 2019. "Stationary distribution for stochastic coupled systems with regime switching and feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    6. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    7. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    8. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    9. Yi, Chengbo & Feng, Jianwen & Wang, Jingyi & Xu, Chen & Zhao, Yi, 2017. "Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 78-90.
    10. Liu, Meng & Bai, Chuanzhi, 2015. "A remark on a stochastic logistic model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 521-526.
    11. Xu, Jiang & Chen, Tao & Wen, Xiangdan, 2021. "Analysis of a Bailey–Dietz model for vector-borne disease under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    12. Luan, Xiaoli & He, Shuping & Liu, Fei, 2009. "Neural network-based robust fault detection for nonlinear jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 760-766.
    13. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    14. Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Pinning impulsive cluster synchronization of uncertain complex dynamical networks with multiple time-varying delays and impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    15. Zhou, Ya & Wan, Xiaoxiao & Huang, Chuangxia & Yang, Xinsong, 2020. "Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    16. Wu, Yongbao & Guo, Haihua & Li, Wenxue, 2020. "Finite-time stabilization of stochastic coupled systems on networks with Markovian switching via feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    17. Wang, Fen & Chen, Yuanlong, 2021. "Mean square exponential stability for stochastic memristor-based neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    18. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    19. Debasis Mukherjee, 2022. "Stochastic Analysis of an Eco-Epidemic Model with Biological Control," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2539-2555, December.
    20. Han, Qixing & Jiang, Daqing, 2015. "Periodic solution for stochastic non-autonomous multispecies Lotka–Volterra mutualism type ecosystem," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 204-217.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:188-195. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.