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Stability of equilibria of exponential type system of three differential equations under stochastic perturbations

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  • Shaikhet, Leonid

Abstract

A system of three differential equations with exponential nonlinearity is considered. It is shown that the considered system has both the zero and nonzero (positive or negative) equilibria. It is supposed that the system is exposed to stochastic perturbations that are directly proportional to the deviation of a system state from an equilibrium. Via the general method of Lyapunov functionals construction and the method of linear matrix inequalities sufficient conditions of stability in probability for an each equilibrium are obtained. Numerical simulations and figures are presented to demonstrate the obtained results. The proposed investigation method can be applied for many other types of nonlinear systems.

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  • Shaikhet, Leonid, 2023. "Stability of equilibria of exponential type system of three differential equations under stochastic perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 105-117.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:105-117
    DOI: 10.1016/j.matcom.2022.11.008
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    References listed on IDEAS

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    1. 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.
    2. Akio Matsumoto & Ferenc Szidarovszky, 2013. "Asymptotic Behavior of a Delay Differential Neoclassical Growth Model," Sustainability, MDPI, vol. 5(2), pages 1-16, January.
    3. 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.
    4. Xiaohua Ding & Wenxue Li, 2006. "Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-12, June.
    5. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
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    Cited by:

    1. Leonid Shaikhet, 2023. "Stability of the Exponential Type System of Stochastic Difference Equations," Mathematics, MDPI, vol. 11(18), pages 1-20, September.

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