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NOVEL STABILITY CONDITIONS FOR SOME GENERALIZATION OF NICHOLSON’S BLOWFLIES MODEL WITH STOCHASTIC PERTURBATIONS

Part of: Applications - Dynamical systems and ergodic theory Functional-differential and differential-difference equations

Published online by Cambridge University Press:  23 August 2023

LEONID SHAIKHET Open the ORCID record for LEONID SHAIKHET [Opens in a new window]  and
SYED ABBAS Open the ORCID record for SYED ABBAS [Opens in a new window]
LEONID SHAIKHET
Affiliation:
Department of Mathematics, Ariel University, Ariel 40700, Israel; e-mail: leonid.shaikhet@usa.net
SYED ABBAS*
Affiliation:
School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Mandi, H.P. 175005, India
*
e-mail: sabbas.iitk@gmail.com
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Abstract

We consider a generalization of the well-known nonlinear Nicholson blowflies model with stochastic perturbations. Stability in probability of the positive equilibrium of the considered equation is studied. Two types of stability conditions: delay-dependent and delay-independent conditions are obtained, using the method of Lyapunov functionals and the method of linear matrix inequalities. The obtained results are illustrated by numerical simulations by means of some examples. The results are new, and complement the existing ones.

Keywords

positive equilibriumstochastic perturbationswhite noisestability in probabilityLyapunov functionalslinear matrix inequality (LMI)numerical simulations

MSC classification

Secondary: 37N25: Dynamical systems in biology 34K20: Stability theory
Type
Research Article
Information
The ANZIAM Journal , Volume 64 , Issue 4 , October 2022 , pp. 394 - 405
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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