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Dynamic System Analysis of Investment in Both Production and R&D with Time Delay

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  • Debao Gao

Abstract

This paper, according to the process of capital return, establishes a differential dynamics model of investment with two time delays. When both time delays are zero, it is proved that the model is positively invariant, uniformly bounded, and globally asymptotically stable by using the comparison principle and Bendixson–Dulac theorem. When at least one time delay is not zero, according to Hopf bifurcation theorem, the conditions of local asymptotic stability and existence of periodic solution of investment model are obtained. By using the normal form theory and the center manifold theory, the discriminant formula of periodic solution property of investment model is given. Under the condition of controlled time delay, the model is numerically simulated to verify the correctness of relevant analytical conclusions. Therefore, the investment model describes the dynamic process and development trend of project investment quite closely.

Suggested Citation

  • Debao Gao, 2022. "Dynamic System Analysis of Investment in Both Production and R&D with Time Delay," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1116671
    DOI: 10.1155/2022/1116671
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    References listed on IDEAS

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    1. Yuri S. Popkov, 2020. "Equilibria and Stability of One Class of Positive Dynamic Systems with Entropy Operator: Application to Investment Dynamics Modeling," Mathematics, MDPI, vol. 8(6), pages 1-15, May.
    2. Yunxian Dai & Yiping Lin & Huitao Zhao, 2014. "Hopf Bifurcation and Global Periodic Solutions in a Predator‐Prey System with Michaelis‐Menten Type Functional Response and Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Yunxian Dai & Yiping Lin & Huitao Zhao, 2014. "Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-16, May.
    4. Bleaney, Michael F., 1996. "Macroeconomic stability, investment and growth in developing countries," Journal of Development Economics, Elsevier, vol. 48(2), pages 461-477, March.
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