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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. Lu Xiao & Huacong Ding & Yu Zhong & Chaojie Wang, 2023. "Optimal Control of Industrial Pollution under Stochastic Differential Models," Sustainability, MDPI, vol. 15(6), pages 1-16, March.
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