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Asymptotic Behavior of Three Connected Stochastic Delay Neoclassical Growth Systems Using Spectral Technique

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  • Ishtiaq Ali

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

  • Sami Ullah Khan

    (Department of Mathematics, City University of Science and Information Technology, Peshawar 2500, KP, Pakistan)

Abstract

In this study, we consider a nonlinear system of three connected delay differential neoclassical growth models along with stochastic effect and additive white noise, which is influenced by stochastic perturbation. We derived the conditions for positive equilibria, stability and positive solutions of the stochastic system. It is observed that when a constant delay reaches a certain threshold for the steady state, the asymptotic stability is lost, and the Hopf bifurcation occurs. In the case of the finite domain, the three connected, delayed systems will not collapse to infinity but will be bounded ultimately. A Legendre spectral collocation method is used for the numerical simulations. Moreover, a comparison of a stochastic delayed system with a deterministic delayed system is also provided. Some numerical test problems are presented to illustrate the effectiveness of the theoretical results. Numerical results further illustrate the obtained stability regions and behavior of stable and unstable solutions of the proposed system.

Suggested Citation

  • Ishtiaq Ali & Sami Ullah Khan, 2022. "Asymptotic Behavior of Three Connected Stochastic Delay Neoclassical Growth Systems Using Spectral Technique," Mathematics, MDPI, vol. 10(19), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3639-:d:933897
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    References listed on IDEAS

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    1. Richard H. Day, 1983. "The Emergence of Chaos from Classical Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 201-213.
    2. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    3. Nataliya Bradul & Leonid Shaikhet, 2007. "Stability of the Positive Point of Equilibrium of Nicholson's Blowflies Equation with Stochastic Perturbations: Numerical Analysis," Discrete Dynamics in Nature and Society, Hindawi, vol. 2007, pages 1-25, August.
    4. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    5. Naseeb Gul & Sami Ullah Khan & Ishtiaq Ali & Farman Ullah Khan, 2022. "Transmission dynamic of stochastic hepatitis C model by spectral collocation method," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 25(5), pages 578-592, April.
    6. Richard H. Day, 1994. "Complex Economic Dynamics - Vol. 1: An Introduction to Dynamical Systems and Market Mechanisms," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041413, April.
    7. Guo, Ying & Li, Yuze, 2022. "Bipartite leader-following synchronization of fractional-order delayed multilayer signed networks by adaptive and impulsive controllers," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    8. Ali, Ishtiaq & Ullah Khan, Sami, 2020. "Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. Akio Matsumoto & Ferenc Szidarovszky, 2013. "Asymptotic Behavior of a Delay Differential Neoclassical Growth Model," Sustainability, MDPI, vol. 5(2), pages 1-16, January.
    10. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
    11. Gian Italo Bischi & Carl Chiarella & Michael Kopel & Ferenc Szidarovszky, 2010. "Nonlinear Oligopolies," Springer Books, Springer, number 978-3-642-02106-0, December.
    12. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    13. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
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    4. Sergei Sitnik, 2023. "Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”," Mathematics, MDPI, vol. 11(15), pages 1-7, August.

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