IDEAS home Printed from https://ideas.repec.org/a/hin/complx/9998756.html
   My bibliography  Save this article

Semi-Analytical Solutions for the Diffusive Kaldor–Kalecki Business Cycle Model with a Time Delay for Gross Product and Capital Stock

Author

Listed:
  • H. Y. Alfifi
  • Baogui Xin

Abstract

This paper discusses the stability and Hopf bifurcation analysis of the diffusive Kaldor–Kalecki model with a delay included in both gross product and capital stock functions. The reaction-diffusion domain is considered, and the Galerkin analytical method is used to derive the system of ordinary differential equations. The methodology used to determine the Hopf bifurcation points is discussed in detail. Furthermore, full diagrams of the Hopf bifurcation regions considered in the stability analysis are shown, and some numerical simulations of the limit cycle are used to confirm the theoretical outcomes. The delay investment parameter and diffusion coefficient can have great impacts on the Hopf bifurcations and stability of the business cycle model. The investment parameters for the gross product and capital stock as well as the adjustment coefficient of the production market are also studied. These parameters can cause instability in, and the stabilization of, the business cycle model. In addition, we point out that, as the delay investment parameter increases, the Hopf bifurcation points for the diffusion coefficient values decrease considerably. When the delay investment parameter has a very small value, the solution of the business cycle model tends to become steady.

Suggested Citation

  • H. Y. Alfifi & Baogui Xin, 2021. "Semi-Analytical Solutions for the Diffusive Kaldor–Kalecki Business Cycle Model with a Time Delay for Gross Product and Capital Stock," Complexity, Hindawi, vol. 2021, pages 1-10, May.
  • Handle: RePEc:hin:complx:9998756
    DOI: 10.1155/2021/9998756
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/complexity/2021/9998756.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/complexity/2021/9998756.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2021/9998756?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
    ---><---

    Citations

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


    Cited by:

    1. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Alfifi, H.Y., 2024. "Stability analysis and Hopf bifurcation for two-species reaction-diffusion-advection competition systems with two time delays," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    3. Alfifi, H.Y., 2023. "Effects of diffusion and delayed immune response on dynamic behavior in a viral model," Applied Mathematics and Computation, Elsevier, vol. 441(C).

    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:hin:complx:9998756. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.