Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes
In this paper, the authors transformed a continuous predator-prey model with modified Leslie-Gower and Holling-type 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, their discrete model shows more irregular and complex dynamic characteristics. The present research can be regarded as the continuation and development of the former studies [\textit{K. Liu} et al., Comput. Math. Methods Med. 2019, Article ID 3859815, 10 p. (2019; Zbl 1423.92198)].
scientific article; zbMATH DE number 7387871
scientific article