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

Leonid Shaikhet

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 206, issue C, 105-117

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.

Keywords: System of nonlinear differential equations; Zero and nonzero equilibria; Stochastic perturbations; Asymptotic mean square stability; Stability in probability; Numerical simulations (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:206:y:2023:i:c:p:105-117

DOI: 10.1016/j.matcom.2022.11.008

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