Open AccessFinite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by L$ {\rm \acute{e}} $vy process with time-varying delay
Author(s) -
Zixiao Xiong,
Xining Li,
Ming Ye,
Qimin Zhang
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021419
Subject(s) - impulse control , impulse (physics) , uniqueness , control theory (sociology) , mathematics , stability (learning theory) , reaction–diffusion system , jump diffusion , jump , control (management) , computer science , mathematical analysis , physics , psychology , quantum mechanics , artificial intelligence , machine learning , psychotherapist
In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and L$ {\rm \acute{e}} $vy 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.