Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy

Zhijun Liu; Jianhua Wu; Yiping Chen; Mainul Haque

doi:10.1016/j.nonrwa.2008.11.017

Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy

Zhijun Liu^*
, Jianhua Wu
, Yiping Chen
, Mainul Haque

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Journal Publication › Article › peer-review

33 Citations (Scopus)

Abstract

In this paper, we consider the dynamic behavior of an impulsive delay differential equation model with the effects of interspecific allelopathic interaction. A good understanding of the permanence, extinction and the existence of positive periodic solutions is gained. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.

Original language	English
Pages (from-to)	432-445
Number of pages	14
Journal	Nonlinear Analysis: Real World Applications
Volume	11
Issue number	1
DOIs	https://doi.org/10.1016/j.nonrwa.2008.11.017
Publication status	Published - Feb 2010

Free Keywords

Delay
Extinction
Impulse
Permanence
Positive periodic solution

ASJC Scopus subject areas

Analysis
General Engineering
General Economics,Econometrics and Finance
Computational Mathematics
Applied Mathematics

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10.1016/j.nonrwa.2008.11.017

Cite this

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title = "Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy",

abstract = "In this paper, we consider the dynamic behavior of an impulsive delay differential equation model with the effects of interspecific allelopathic interaction. A good understanding of the permanence, extinction and the existence of positive periodic solutions is gained. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.",

keywords = "Delay, Extinction, Impulse, Permanence, Positive periodic solution",

author = "Zhijun Liu and Jianhua Wu and Yiping Chen and Mainul Haque",

note = "Funding Information: The work is supported by the Project of China Postdoctoral Science Foundation (20080431227), the Natural Science Foundation of Hubei Province of China and the Innovation Term of Educational Department of Hubei Province of China (T200804, Q20082906). We would like to thank the referees for their careful reading of the original manuscript and their valuable comments and suggestions that greatly improved the presentation of this work. ",

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T1 - Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy

AU - Liu, Zhijun

AU - Wu, Jianhua

AU - Chen, Yiping

AU - Haque, Mainul

N1 - Funding Information: The work is supported by the Project of China Postdoctoral Science Foundation (20080431227), the Natural Science Foundation of Hubei Province of China and the Innovation Term of Educational Department of Hubei Province of China (T200804, Q20082906). We would like to thank the referees for their careful reading of the original manuscript and their valuable comments and suggestions that greatly improved the presentation of this work.

PY - 2010/2

Y1 - 2010/2

N2 - In this paper, we consider the dynamic behavior of an impulsive delay differential equation model with the effects of interspecific allelopathic interaction. A good understanding of the permanence, extinction and the existence of positive periodic solutions is gained. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.

AB - In this paper, we consider the dynamic behavior of an impulsive delay differential equation model with the effects of interspecific allelopathic interaction. A good understanding of the permanence, extinction and the existence of positive periodic solutions is gained. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.

KW - Delay

KW - Extinction

KW - Impulse

KW - Permanence

KW - Positive periodic solution

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DO - 10.1016/j.nonrwa.2008.11.017

M3 - Article

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SN - 1468-1218

VL - 11

SP - 432

EP - 445

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 1

ER -

Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy

Abstract

Free Keywords

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