Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay

In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and Lévy jump is proposed. The existence and uniqueness of the positive solution are proved. Meanwhile, mainly through the principle of comparison, we obtain the sufficient conditions for finite-time stabili...

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Autores principales:	Zixiao Xiong, Xining Li, Ming Ye, Qimin Zhang
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	vegetation-water model optimal control finite-time stability lévy process Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e8697770f6d74e8d874095552b5fe790
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spelling	oai:doaj.org-article:e8697770f6d74e8d874095552b5fe7902021-11-24T01:31:07ZFinite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay10.3934/mbe.20214191551-0018https://doaj.org/article/e8697770f6d74e8d874095552b5fe7902021-09-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021419?viewType=HTMLhttps://doaj.org/toc/1551-0018In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and Lévy jump is proposed. The existence and uniqueness of the positive solution are proved. Meanwhile, mainly through the principle of comparison, we obtain the sufficient conditions for finite-time stability which reflect the effect of time delay, diffusion, impulse, and noise. Besides, considering the planting, irrigation and other measures, we introduce control variable into the vegetation-water system. In order to save the costs of strategies, the optimal control is analyzed by using the minimum principle. Finally, numerical simulations are shown to illustrate the effectiveness of our theoretical results.Zixiao XiongXining LiMing YeQimin ZhangAIMS Pressarticlevegetation-water modeloptimal controlfinite-time stabilitylévy processBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 8462-8498 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	vegetation-water model optimal control finite-time stability lévy process Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	vegetation-water model optimal control finite-time stability lévy process Biotechnology TP248.13-248.65 Mathematics QA1-939 Zixiao Xiong Xining Li Ming Ye Qimin Zhang Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay
description	In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and Lévy jump is proposed. The existence and uniqueness of the positive solution are proved. Meanwhile, mainly through the principle of comparison, we obtain the sufficient conditions for finite-time stability which reflect the effect of time delay, diffusion, impulse, and noise. Besides, considering the planting, irrigation and other measures, we introduce control variable into the vegetation-water system. In order to save the costs of strategies, the optimal control is analyzed by using the minimum principle. Finally, numerical simulations are shown to illustrate the effectiveness of our theoretical results.
format	article
author	Zixiao Xiong Xining Li Ming Ye Qimin Zhang
author_facet	Zixiao Xiong Xining Li Ming Ye Qimin Zhang
author_sort	Zixiao Xiong
title	Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay
title_short	Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay
title_full	Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay
title_fullStr	Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay
title_full_unstemmed	Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay
title_sort	finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by lévy process with time-varying delay
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/e8697770f6d74e8d874095552b5fe790
work_keys_str_mv	AT zixiaoxiong finitetimestabilityandoptimalcontrolofanimpulsivestochasticreactiondiffusionvegetationwatersystemdrivenbylevyprocesswithtimevaryingdelay AT xiningli finitetimestabilityandoptimalcontrolofanimpulsivestochasticreactiondiffusionvegetationwatersystemdrivenbylevyprocesswithtimevaryingdelay AT mingye finitetimestabilityandoptimalcontrolofanimpulsivestochasticreactiondiffusionvegetationwatersystemdrivenbylevyprocesswithtimevaryingdelay AT qiminzhang finitetimestabilityandoptimalcontrolofanimpulsivestochasticreactiondiffusionvegetationwatersystemdrivenbylevyprocesswithtimevaryingdelay
_version_	1718416066892267520

Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay

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