IDEAS home Printed from https://ideas.repec.org/a/wly/jjmath/v2022y2022i1n3466954.html

Dynamic Analysis on a Diffusive Two‐Enterprise Interaction Model with Two Delays

Author

Listed:
  • Yanxia Zhang
  • Long Li

Abstract

The oscillation and instability of systems caused by time delays have been widely studied over the past several decades. In nature, the phenomenon of diffusion is universal. Therefore, it is necessary to investigate the dynamic behavior of reaction‐diffusion systems with time delays. In this study, a two‐enterprise interaction model with diffusion and delay effects is considered. By analyzing the distribution of the roots of the corresponding characteristic equation, some conditions for the stability of the unique positive equilibrium and the existence of Hopf bifurcation at the steady state are investigated. As the sum of the time delays changes, there are a series of periodic solutions at the trivial steady‐state solution of the system. In addition, the direction of Hopf bifurcation and the stability of the periodic solutions are discussed by using the normal form theory and the center manifold reduction of partial functional differential equations. Finally, numerical simulation experiments are conducted to illustrate the validity of the theoretical conclusions.

Suggested Citation

  • Yanxia Zhang & Long Li, 2022. "Dynamic Analysis on a Diffusive Two‐Enterprise Interaction Model with Two Delays," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3466954
    DOI: 10.1155/2022/3466954
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/3466954
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/3466954?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
    ---><---

    References listed on IDEAS

    as
    1. Liu, Fuxiang & Yang, Ruizhi & Tang, Leiyu, 2019. "Hopf bifurcation in a diffusive predator-prey model with competitive interference," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 250-258.
    2. Hu, Haijun & Tan, Yanxiang & Huang, Jianhua, 2019. "Hopf bifurcation analysis on a delayed reaction-diffusion system modelling the spatial spread of bacterial and viral diseases," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 152-162.
    3. Han, Renji & Dai, Binxiang, 2017. "Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 90-109.
    4. Wenjie Hu & Hua Zhao & Tao Dong, 2018. "Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect," Complexity, Hindawi, vol. 2018, pages 1-11, January.
    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. Li, Wenjie & Guan, Yajuan & Cao, Jinde & Xu, Fei, 2024. "Global dynamics and threshold control of a discontinuous fishery ecological system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    3. Ma, Zhan-Ping & Yue, Jia-Long, 2023. "Cross diffusion induced spatially inhomogeneous Hopf bifurcation for a three species Lotka–Volterra food web model with cycle," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jjmath:v:2022:y:2022:i:1:n:3466954. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/1469 .

    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.