IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v179y2024ics0960077924000286.html
   My bibliography  Save this article

Existence of stationary distribution for stochastic coupled nonlinear strict-feedback systems with Markovian switching

Author

Listed:
  • Guo, Wanying
  • Meng, Shuyu
  • Qi, Ruotong
  • Li, Wenxue
  • Wu, Yongbao

Abstract

In this paper, a class of stochastic coupled nonlinear strict-feedback systems with Markovian switching (SCNSSMs) are introduced, and the existence of stationary distribution for SCNSSMs under pinning control is studied for the first time. In particular, an appropriate technique for handling the impact of Markovian switching is proposed in the process of designing virtual controllers through the back-stepping method. Regarding the global Lyapunov function for an SCNSSM, we first construct a quartic Lyapunov function for each stochastic nonlinear strict-feedback system with Markovian switching of the SCNSSM, and then combine graph theory to construct the global Lyapunov function. After that, the theoretical results are applied to stochastic coupled oscillator systems with Markovian switching. Finally, the effectiveness of proposed results is verified by some numerical simulations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s0960077924000286
    DOI: 10.1016/j.chaos.2024.114477
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924000286
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114477?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. Treur, Jan, 2020. "Analysis of a network’s asymptotic behavior via its structure involving its strongly connected components," Network Science, Cambridge University Press, vol. 8(S1), pages 82-109, July.
    3. Parastesh, Fatemeh & Azarnoush, Hamed & Jafari, Sajad & Hatef, Boshra & Perc, Matjaž & Repnik, Robert, 2019. "Synchronizability of two neurons with switching in the coupling," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 217-223.
    4. 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.
    5. Li, Jiayang & Zhang, Zhikun & Dai, Min & Ming, Ju & Wang, Xiangjun, 2023. "Diffusion equations with Markovian switching: Well-posedness, numerical generation and parameter inference," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    6. Yang, Ni & Gao, Ruiyi & Su, Huan, 2022. "Stability of multi-links complex-valued impulsive stochastic systems with Markovian switching and multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Boukanjime, Brahim & Caraballo, Tomás & El Fatini, Mohamed & El Khalifi, Mohamed, 2020. "Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    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. 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.
    2. 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).
    3. Nikolaos P. Rachaniotis & Thomas K. Dasaklis & Filippos Fotopoulos & Platon Tinios, 2021. "A Two-Phase Stochastic Dynamic Model for COVID-19 Mid-Term Policy Recommendations in Greece: A Pathway towards Mass Vaccination," IJERPH, MDPI, vol. 18(5), pages 1-21, March.
    4. 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.
    5. 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).
    6. Yu, Xihong & Bao, Han & Chen, Mo & Bao, Bocheng, 2023. "Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    7. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    8. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. 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).
    10. Faik Bilgili & Emrah Koçak & Sevda Kuşkaya, 2023. "Dynamics and Co-movements Between the COVID-19 Outbreak and the Stock Market in Latin American Countries: An Evaluation Based on the Wavelet-Partial Wavelet Coherence Model," Evaluation Review, , vol. 47(4), pages 630-652, August.
    11. 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).
    12. Kafraj, Mohadeseh Shafiei & Parastesh, Fatemeh & Jafari, Sajad, 2020. "Firing patterns of an improved Izhikevich neuron model under the effect of electromagnetic induction and noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    13. 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.
    14. Feng, Jiqiang & Li, Yongcai & Zhang, Yingfang & Xu, Chen, 2023. "Stabilization of multi-link delayed neutral-type complex networks with jump diffusion via aperiodically intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    15. Guo, Wenjuan & Zhang, Qimin, 2021. "Explicit numerical approximation for an impulsive stochastic age-structured HIV infection model with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 86-115.
    16. Li, Qiang & Kang, Ting & Zhang, Qimin, 2018. "Mean-square dissipative methods for stochastic age-dependent capital system with fractional Brownian motion and jumps," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 81-92.
    17. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution of a stochastic predator–prey system with stage structure for prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    18. Wen, Buyu & Rifhat, Ramziya & Teng, Zhidong, 2019. "The stationary distribution in a stochastic SIS epidemic model with general nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 258-271.
    19. Zeng, Ting & Teng, Zhidong & Li, Zhiming & Hu, Junna, 2018. "Stability in the mean of a stochastic three species food chain model with general Le´vy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 258-265.
    20. Wang, Zhixiao & Rui, Xiaobin & Yuan, Guan & Cui, Jingjing & Hadzibeganovic, Tarik, 2021. "Endemic information-contagion outbreaks in complex networks with potential spreaders based recurrent-state transmission dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

    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:179:y:2024:i:c:s0960077924000286. 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.