Version 1
: Received: 25 September 2024 / Approved: 25 September 2024 / Online: 26 September 2024 (09:12:14 CEST)
How to cite:
Shaikhet, L. About Stability of One System of Stochastic Difference Equations with Exponential Nonlinearity. Preprints2024, 2024092043. https://doi.org/10.20944/preprints202409.2043.v1
Shaikhet, L. About Stability of One System of Stochastic Difference Equations with Exponential Nonlinearity. Preprints 2024, 2024092043. https://doi.org/10.20944/preprints202409.2043.v1
Shaikhet, L. About Stability of One System of Stochastic Difference Equations with Exponential Nonlinearity. Preprints2024, 2024092043. https://doi.org/10.20944/preprints202409.2043.v1
APA Style
Shaikhet, L. (2024). About Stability of One System of Stochastic Difference Equations with Exponential Nonlinearity. Preprints. https://doi.org/10.20944/preprints202409.2043.v1
Chicago/Turabian Style
Shaikhet, L. 2024 "About Stability of One System of Stochastic Difference Equations with Exponential Nonlinearity" Preprints. https://doi.org/10.20944/preprints202409.2043.v1
Abstract
A system of two nonlinear difference equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on all variables of the system. The stability in probability of a positive equilibrium of the system is studied via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic difference equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, for both difference equations and for delay differential equations.
Keywords
nonlinear difference equations; positive equilibrium; stochastic perturbations; asymptotic mean square stability; stability in probability; linear matrix inequality (LMI); numerical simulations; MATLAB
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
