School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China.
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA.
Math Biosci Eng. 2021 Sep 27;18(6):8462-8498. doi: 10.3934/mbe.2021419.
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.
本文提出了一个具有时变时滞、脉冲和 Lévy 跳跃的反应扩散植被-水系统。证明了正解的存在唯一性。同时，主要通过比较原理，得到了反映时滞、扩散、脉冲和噪声影响的有限时间稳定性的充分条件。此外，考虑到种植、灌溉等措施，我们将控制变量引入到植被-水系统中。为了节省策略的成本，我们使用最小原理对最优控制进行了分析。最后，通过数值模拟验证了我们理论结果的有效性。
