Finite-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

In this paper, deterministic and stochastic reaction-diffusion vege-tation-water systems with time-varying delay are developed, respectively. For the deterministic system, we define a threshold <inline-formula><tex-math id="M1">\begin{document}$ R_* $\end{document}</tex-math></inline-formula> and discuss the threshold dynamics of the system. When <inline-formula><tex-math id="M2">\begin{document}$ R_*<1 $\end{document}</tex-math></inline-formula>, the vegetation-free equilibrium point of the system is locally asymptotically stable. For <inline-formula><tex-math id="M3">\begin{document}$ R_*>1 $\end{document}</tex-math></inline-formula>, the vegetation is persistent. Besides, by Latin Hypercube Sampling (LHS) and partial rank correlation coefficients (PRCCs), global sensitivity analysis is shown. For the stochastic system driven by Markov switching and Gaussian noise, with the help of stochastic comparison principle, several sufficient conditions are obtained to ensure the finite-time stability and finite time contractive stability. Numerical simulations are carried out to support the effectiveness of theoretical results.

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Impulsive strategies in nonlinear dynamical systems: A brief overview

Zhu

2022

MBE

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<abstract>The studies of impulsive dynamical systems have been thoroughly explored, and extensive publications have been made available. This study is mainly in the framework of continuous-time systems and aims to give an exhaustive review of several main kinds of impulsive strategies with different structures. Particularly, (i) two kinds of impulse-delay structures are discussed respectively according to the different parts where the time delay exists, and some potential effects of time delay in stability analysis are emphasized. (ii) The event-based impulsive control strategies are systematically introduced in the light of several novel event-triggered mechanisms determining the impulsive time sequences. (iii) The hybrid effects of impulses are emphatically stressed for nonlinear dynamical systems, and the constraint relationships between different impulses are revealed. (iv) The recent applications of impulses in the synchronization problem of dynamical networks are investigated. Based on the above several points, we make a detailed introduction for impulsive dynamical systems, and some significant stability results have been presented. Finally, several challenges are suggested for future works.</abstract>

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Finite-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

Cited by 4 publications

References 47 publications

Persistence and extinction of a reaction–diffusion vegetation-water system with time–space white noise

Persistence and extinction of a reaction–diffusion vegetation-water system with time–space white noise

Threshold dynamics and finite-time stability of reaction-diffusion vegetation-water systems in arid area with time-varying delay

Impulsive strategies in nonlinear dynamical systems: A brief overview

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