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Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes.
Mathematical Biosciences and Engineering ( IF 2.6 ) Pub Date : 2019-12-23 , DOI: 10.3934/mbe.2020106
Yang Yang Li 1 , Feng Xue Zhang 1 , Xiang Lai Zhuo 2
Affiliation  

The continuous predator-prey model is one of the main models studied in recent years. The dynamical properties of these models are so complex that it is an urgent topic to be studied. In this paper, we transformed a continuous predator-prey model with modified Leslie-Gower and Hollingtype III schemes into a discrete mode by using Euler approximation method. The existence and stability of fixed points for this discrete model were investigated. Flip bifurcation analyses of this discrete model was carried out and corresponding bifurcation conditions were obtained. Provided with these bifurcation conditions, an example was given to carry out numerical simulations, which shows that the discrete model undergoes flip bifurcation around the stable fixed point. In addition, compared with previous studies on the continuous predator-prey model, our discrete model shows more irregular and complex dynamic characteristics. The present research can be regarded as the continuation and development of the former studies.

中文翻译:

具有改进的Leslie-Gower和Holling-type III方案的离散捕食者-食饵模型的翻转分叉。

连续捕食-被捕食模型是近年来研究的主要模型之一。这些模型的动力学特性是如此复杂,以至于它是一个亟待研究的课题。在本文中,我们使用欧拉逼近法将具有改进的莱斯利-高尔和Hollingtype III方案的连续捕食者-食饵模型转换为离散模式。研究了该离散模型不动点的存在性和稳定性。对该离散模型进行了翻转分叉分析,并获得了相应的分叉条件。在提供这些分叉条件的情况下,给出了一个进行数值模拟的例子,这表明离散模型在稳定的固定点附近经历了翻转分叉。另外,与之前关于连续捕食者-猎物模型的研究相比,我们的离散模型显示出更多不规则和复杂的动态特征。本研究可以看作是对以前研究的延续和发展。
更新日期:2019-12-23
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