SLIDING BIFURCATIONS OF FILIPPOV TWO STAGE PEST CONTROL MODELS WITH ECONOMIC THRESHOLDS
SLIDING BIFURCATIONS OF FILIPPOV TWO STAGE PEST CONTROL MODELS WITH ECONOMIC THRESHOLDS
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具有经济阈值的FILIPPOV两阶段害虫防治模型的滑动分支
DOI：
10.1137/110847020
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发表时间：
2012-01-01
影响因子：
1.9
通讯作者：
Cheke, Robert A.
中科院分区：
文献类型：
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作者：
Tang, Sanyi;Liang, Juhua;Cheke, Robert A.
为了控制害虫，提出了一种称为阈值策略的特定管理策略，该策略可以用Filippov系统（或分段光滑系统）来描述。本文研究了具有密度依赖的人均出生率和从幼年种群到成年种群的过渡率的Filippov两阶段结构种群模型的平衡点和滑动环的分歧现象。结果表明，interadult竞争单独可以引起多个滑动段和多个伪平衡，而interadult和interjuvenile竞争一起可以导致丰富的滑动分叉。当阈值变化时，系统将依次出现包括边界节点（鞍点）、相切和伪鞍点分叉在内的局部滑动分叉，以及包括滑动环屈曲分叉、滑动交叉分叉和伪同宿分叉在内的全局滑动分叉.阈值策略控制在害虫管理中已被证明是容易实施和有用的，其可用于防止多个害虫爆发的可能性或使害虫密度稳定在期望的水平（诸如经济阈值）。
In order to control pests, a specific management strategy called the threshold policy is proposed, which can be described by Filippov systems (or piecewise smooth systems). The aim of this work is to investigate a variety of bifurcation phenomena of the equilibria and sliding cycles of Filippov two stage structured population models with density dependent per capita birth rates and transition rates from the juvenile class into the adult class. It is shown that interadult competition alone can give rise to multiple sliding segments and multiple pseudoequilibria, whilst interadult and interjuvenile competition together can result in rich sliding bifurcations. As the threshold value varies, local sliding bifurcations including boundary node (saddle), tangency, and pseudo-saddle-node bifurcations occur sequentially, and global sliding bifurcations including buckling bifurcations of the sliding cycles, sliding crossing bifurcations, and pseudohomoclinic bifurcations can be present. Threshold policy control has been shown to be easily implemented and useful in pest management, which can be used to prevent the possibility of multiple pest outbreaks or cause the density of pests to stabilize at a desired level such as an economic threshold.