About Stability Investigation of a System of Two Nicholson's Blowflies Equations Under Stochastic Perturbations

8 Pages Posted: 26 Dec 2023

Abstract

A method of stability investigation for stochastic nonlinear dynamical systems with delays is demonstrated on a system of two connected Nicholson's blowflies equations. It is supposed that this system is affected by stochastic perturbations of the white noise type that are directly proportional to the deviation of the system state from the equilibrium. Stability conditions for the zero and positive equilibria of the system under consideration are obtained by virtue of the general method of Lyapunov functionals construction and are formulated in terms of Linear Matrix Inequalities (LMIs), that can be checked by MATLAB. Numerical examples and figures illustrate the obtained theoretical results.

Keywords: Zero and positive equilibria, Stochastic perturbations, Lyapunov functionals, Linear Matrix Inequality (LMI), Numerical simulations

Suggested Citation

Shaikhet, Leonid, About Stability Investigation of a System of Two Nicholson's Blowflies Equations Under Stochastic Perturbations. Available at SSRN: https://ssrn.com/abstract=4676233 or http://dx.doi.org/10.2139/ssrn.4676233

Leonid Shaikhet (Contact Author)

Ariel University ( email )

Israel

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