Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations
This paper is concerned with the stability problem of the positive equilibrium of a Nicholson's blowflies model with nonlinear density-dependent mortality rate subject to stochastic perturbations. More specifically, the existence of a unique positive equilibrium of a Nicholson's blowflies...
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University of Szeged
2020-04-01
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doaj-02544ab97e24457382c9b6b113f248732021-07-14T07:21:33ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752020-04-0120202111110.14232/ejqtde.2020.1.217908Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbationsLe Van Hien0Nguyen Thi Lan-Huong1Department of Mathematics, Hanoi National University of Education, Hanoi, VietnamHanoi National University of Education, Hanoi, VietnamThis paper is concerned with the stability problem of the positive equilibrium of a Nicholson's blowflies model with nonlinear density-dependent mortality rate subject to stochastic perturbations. More specifically, the existence of a unique positive equilibrium of a Nicholson's blowflies model described by the delay differential equation \begin{equation*} N'(t)=-\left(a-be^{-N(t)}\right)+\beta N(t-\tau)e^{-\gamma N(t-\tau)} \end{equation*} is first quoted. It is assumed that the underlying model in noisy environments is exposed to stochastic perturbations, which are proportional to the derivation of the state from the equilibrium point. Then, by utilizing a stability criterion formulated for linear stochastic differential delay equations, explicit stability conditions are obtained. An extension to models with multiple delays is also presented.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7908nicholson's blowflies modelnonlinear mortality ratestochastic perturbationsasymptotic stability |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Le Van Hien Nguyen Thi Lan-Huong |
spellingShingle |
Le Van Hien Nguyen Thi Lan-Huong Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations Electronic Journal of Qualitative Theory of Differential Equations nicholson's blowflies model nonlinear mortality rate stochastic perturbations asymptotic stability |
author_facet |
Le Van Hien Nguyen Thi Lan-Huong |
author_sort |
Le Van Hien |
title |
Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations |
title_short |
Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations |
title_full |
Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations |
title_fullStr |
Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations |
title_full_unstemmed |
Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations |
title_sort |
stability of positive equilibrium of a nicholson blowflies model with stochastic perturbations |
publisher |
University of Szeged |
series |
Electronic Journal of Qualitative Theory of Differential Equations |
issn |
1417-3875 1417-3875 |
publishDate |
2020-04-01 |
description |
This paper is concerned with the stability problem of the positive equilibrium of a Nicholson's blowflies model with nonlinear density-dependent mortality rate subject to stochastic perturbations. More specifically, the existence of a unique positive equilibrium of a Nicholson's blowflies model described by the delay differential equation
\begin{equation*}
N'(t)=-\left(a-be^{-N(t)}\right)+\beta N(t-\tau)e^{-\gamma N(t-\tau)}
\end{equation*}
is first quoted. It is assumed that the underlying model in noisy environments is exposed to stochastic perturbations, which are proportional to the derivation of the state from the equilibrium point. Then, by utilizing a stability criterion formulated for linear stochastic differential delay equations, explicit stability conditions are obtained. An extension to models with multiple delays is also presented. |
topic |
nicholson's blowflies model nonlinear mortality rate stochastic perturbations asymptotic stability |
url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7908 |
work_keys_str_mv |
AT levanhien stabilityofpositiveequilibriumofanicholsonblowfliesmodelwithstochasticperturbations AT nguyenthilanhuong stabilityofpositiveequilibriumofanicholsonblowfliesmodelwithstochasticperturbations |
_version_ |
1721303319936237568 |