### Mathematical Biosciences and Engineering

2020, Issue 3: 2003-2015. doi: 10.3934/mbe.2020106
Research article

# Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes

• Received: 10 October 2019 Accepted: 12 December 2019 Published: 23 December 2019
• 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.

Citation: Yangyang Li, Fengxue Zhang, Xianglai Zhuo. Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2003-2015. doi: 10.3934/mbe.2020106

### Related Papers:

• 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.

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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