A reaction-diffusion population growth equation with multiple pulse perturbations
A reaction-diffusion population growth equation with multiple pulse perturbations
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具有多个脉冲扰动的反应扩散群体增长方程
DOI：
10.1016/j.cnsns.2019.02.015
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发表时间：
2019-07
影响因子：
3.9
通讯作者：
Tang Sanyi
中科院分区：
文献类型：
--
作者：
Liang Juhua;Yan Qian;Xiang Changcheng;Tang Sanyi
在害虫生长世代期间，存在许多内部和外部扰动，包括出生脉冲和脉冲杀虫剂施用，由于扰动时间的变化，导致每个害虫生长世代内的复杂生长模式。为了展示多重脉冲扰动如何影响害虫种群的动态，我们通过涉及即时出生和控制扰动扩展了经典的费舍尔反应扩散方程。主要结果表明，脉冲扰动对空间齐次周期解的存在性和稳定性有显着影响。特别是，出生率和杀灭效力会影响行波及其传播速度，而农药施用的时机对这些阈值条件没有任何影响。然而，数值调查表明，农药施用的时间可以显着影响害虫种群的空间分布。在每一代中，过早或过晚施用农药都可能导致害虫生长更快、传播范围更广，最佳施药时机是每代中期，此时农药药效相对较低。分叉分析表明偶数代和奇数代表现出不同的空间格局，这反映了与害虫控制和害虫管理相关的一些重要问题，例如偶数代和奇数代应采取不同的控制策略。为了解决空间异质性对害虫防治成本的影响，我们进一步制定成本函数来研究最佳害虫防治策略，并在数值上获得了使成本最小化的最佳空间依赖性杀灭率。
During the pest growth generations there exist a number of internal and external perturbations including birth pulses and pulse pesticide applications, which result in a complex growth pattern within each pest growth generation due to the variation of perturbation timings. In order to show how multiple pulse perturbations affect the dynamics of the pest population, we have extended the classical Fisher reaction-diffusion equation by involving instant birth and control perturbations. The main results indicate that the pulse perturbations have a remarkable influence on the existence and stability of a spatially homogeneous periodic solution. In particular, the birth rate and killing efficacy can affect the traveling wave and its spreading speed, while the timing of pesticide application does not make any effects on those threshold conditions. However, numerical investigations reveal that the timing of pesticide applications can significantly affect the spatial distributions of the pest population. Within each generation too early or too late pesticide application could result in a faster growth and wider spread of the pest, and the optimal timing of pesticide application is the middle of each generation provided that the efficacy of the pesticide is relatively low. Bifurcation analyses reveal that even generations and odd generations display a different spatial pattern, which depict some important issues related to the pest control and pest management, for example the different control strategies should be adopted for even and odd generations. To address how the spatial heterogeneity affects on the cost of the pest control, we further formulate the cost function to investigate the optimal pest control strategy, and the optimal spatial dependent killing rates which minimize the cost have been obtained numerically.
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DOI：
--
发表时间：
2016
期刊：
--
影响因子：
--
作者：
Sanyi Tang;Guangyao Tang;R. Cheke
通讯作者：
Sanyi Tang;Guangyao Tang;R. Cheke
影响因子：
2.4
作者：
Xiaoqing He;W. Ni
通讯作者：
Xiaoqing He;W. Ni
DOI：
10.1111/0002-9092.00044
发表时间：
2000-08
期刊：
Health Economics eJournal
影响因子：
--
作者：
David L. Sunding;J. Zivin
通讯作者：
David L. Sunding;J. Zivin
描述脉冲集满足次数函数的连续性及其应用
影响因子：
2.6
作者：
Tang, Sanyi;Pang, Wenhong
通讯作者：
Pang, Wenhong
影响因子：
3.5
作者：
M. Lewis;Bingtuan Li
通讯作者：
M. Lewis;Bingtuan Li