IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v354y2019icp396-410.html
   My bibliography  Save this article

Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations

Author

Listed:
  • Luo, Tianjiao

Abstract

This paper focuses on the multi-group models with multiple dispersal and stochastic perturbation (MGMDS). The effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration. The stabilization of MGMDS is investigated via feedback control based on the discrete-time state observations. In addition, a systematic method is given to construct a global Lyapunov function for MGMDS. By means of graph theory and Lyapunov method, some sufficient conditions are obtained to ensure the stabilization in the sense of mean-square asymptotical stability. An upper bound of the duration between two consecutive state observations is estimated. Moreover, to show the applicability of our results, the main theory is employed to a stochastic coupled oscillators. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results.

Suggested Citation

  • Luo, Tianjiao, 2019. "Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 396-410.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:396-410
    DOI: 10.1016/j.amc.2019.01.052
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319300670
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.01.052?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. Xiaoming Fan, 2014. "Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, January.
    2. Ahmad, Iftikhar & Mukhtar, Areej, 2015. "Stochastic approach for the solution of multi-pantograph differential equation arising in cell-growth model," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 360-372.
    3. Qiu, Qinwei & Liu, Wei & Hu, Liangjian & Mao, Xuerong & You, Surong, 2016. "Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay," Statistics & Probability Letters, Elsevier, vol. 115(C), pages 16-26.
    4. Chen, Liping & Wu, Ranchao & He, Yigang & Yin, Lisheng, 2015. "Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 274-284.
    5. dos Santos, Angela M. & Lopes, Sergio R. & Viana, R.L.Ricardo L., 2004. "Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 335-355.
    6. Nagamani, G. & Ramasamy, S., 2016. "Stochastic dissipativity and passivity analysis for discrete-time neural networks with probabilistic time-varying delays in the leakage term," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 237-257.
    7. Lu, Jun Guo & Chen, Guanrong, 2009. "Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2293-2300.
    8. Wang, Guoliang & Cai, Hongyang & Zhang, Qingling & Yang, Chunyu, 2017. "Stabilization of stochastic delay systems via a disordered controller," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 98-109.
    9. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
    10. Aihua Hu & Jinde Cao & Manfeng Hu & Liuxiao Guo, 2016. "Distributed control of cluster synchronisation in networks with randomly occurring non-linearities," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2588-2597, August.
    Full references (including those not matched with items on IDEAS)

    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. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. dos Santos, A.M. & Lopes, S.R. & Viana, R.L., 2008. "Synchronization regimes for two coupled noisy Liénard-type driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 901-910.
    3. Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    4. Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Lin, Wen-Juan & Wu, Min, 2017. "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 102-120.
    5. 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).
    6. Dong, Tao & Wang, Aijuan & Zhu, Huiyun & Liao, Xiaofeng, 2018. "Event-triggered synchronization for reaction–diffusion complex networks via random sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 454-462.
    7. Zhang, Tian & Chen, Huabin, 2019. "The stability with a general decay of stochastic delay differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 294-307.
    8. Feng, Lichao & Liu, Qiumei & Cao, Jinde & Zhang, Chunyan & Alsaadi, Fawaz, 2022. "Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    9. Acosta, A. & Gallo, R. & García, P. & Peluffo-Ordóñez, D., 2023. "Positive invariant regions for a modified Van Der Pol equation modeling heart action," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    10. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2007. "Chaos in a generalized van der Pol system and in its fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1711-1745.
    11. Yu, Peilin & Deng, Feiqi, 2022. "Stabilization analysis of Markovian asynchronous switched systems with input delay and Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    12. Mukama, Denis Sospeter & Ghani, Mohammad & Mbalawata, Isambi Sailon, 2023. "Persistence, Extinction, and boundedness in pth moment of hybrid stochastic logistic systems by delay feedback control based on discrete-time observation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 661-677.
    13. Ezz-Eldien, S.S., 2018. "On solving systems of multi-pantograph equations via spectral tau method," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 63-73.
    14. Der-Fa Chen & Yi-Cheng Shih & Shih-Cheng Li & Chin-Tung Chen & Jung-Chu Ting, 2020. "Mixed Modified Recurring Rogers-Szego Polynomials Neural Network Control with Mended Grey Wolf Optimization Applied in SIM Expelling System," Mathematics, MDPI, vol. 8(5), pages 1-28, May.
    15. Lounis, Fatima & Boukabou, Abdelkrim & Soukkou, Ammar, 2020. "Implementing high-order chaos control scheme for cardiac conduction model with pathological rhythms," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    16. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
    17. Zhang, Lan & Yang, Xinsong & Xu, Chen & Feng, Jianwen, 2017. "Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 22-30.
    18. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    19. Shan, Yaonan & She, Kun & Zhong, Shouming & Zhong, Qishui & Shi, Kaibo & Zhao, Can, 2018. "Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 145-168.
    20. Fei Qi & Yi Chai & Liping Chen & José A. Tenreiro Machado, 2020. "Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems," Mathematics, MDPI, vol. 9(1), pages 1-13, December.

    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:apmaco:v:354:y:2019:i:c:p:396-410. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.