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首页> 外文期刊>Applied Mathematical Modelling >Allee effect in prey's growth reduces the dynamical complexity in prey-predator model with generalist predator
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Allee effect in prey's growth reduces the dynamical complexity in prey-predator model with generalist predator

机译：在猎物的增长中的Allee效应降低了与通用捕食者的猎物捕食者模型中的动态复杂性

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摘要

Prey-predator models with Allee effect have great importance in the context of ecology. Allee effect refers to a positive relationship between population density and per capita growth rate. Here we examine the influences of Allee effect in a prey-predator interaction model with a generalist predator. First we consider a prey-predator model with a generalist predator without the Allee effect which exhibits rich and complex dynamics like bistability, tristability along with local and global bifurcations such as cyclic bifurcations of limit cycle, homoclinic bifurcation, etc. Next, we investigate the same model with Allee effect in prey's growth. This modified model exhibits simpler dynamics compared to the previous model. Though it undergoes local and global bifurcations as in the previous model, but tristability does not occur in this model. Also, increase of Allee parameter turns the system more structurally stable compared to prey-predator model with generalist predator only. Some of the results are supported numerically since the interior equilibrium points can not be obtained analytically.
机译：在生态学的背景下，捕食性捕食者模型具有重要意义。 Allee效应是指人口密度与人均增长率之间的正相关关系。在这里，我们研究了与通用捕食者在猎物捕食者交互模型中的影响。首先，我们考虑一个具有通用捕食者的猎物捕食者模型，没有含有富有的和复杂的动态，如双稳态，诸如极限循环的循环分叉等局部和全球分叉等的诸如局部和全球分岔等的植物效果。接下来，我们调查相同模型与猎物增长的含量效应。与以前的模型相比，这种修改的模型表现出更简单的动态。虽然它在以前的模型中经历了本地和全球分叉，但在此模型中不会发生三批故。此外，与具有通用捕食者的猎物预捕食者模型相比，Allee参数的增加将更加结构稳定。由于无法分析地获得内部平衡点，因此数值支持一些结果。

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