@article{Xia2022, 
author = {Shaosan Xia and Xianyi Li},
title = {Complicate dynamics of a discrete predator-prey model with double Allee effect},
year = {2022},
journal = {Mathematical Modelling and Control},
volume = {2},
number = {4},
pages = {282-295},
keywords = {Neimark-Sacker bifurcation, transcritical bifurcation, discrete predator-prey system, double Allee effect},
url = {https://www.sciopen.com/article/10.3934/mmc.2022027},
doi = {10.3934/mmc.2022027},
abstract = {In this paper, a discrete predator-prey model with double Allee effect is discussed. We first simplify the corresponding continuous predator-prey model, and use the semidiscretization method to obtain a new discrete model. Next, the existence and local stability of nonnegative fixed points of the new discrete model are studied by using a key lemma. Then, by using the center manifold theorem and bifurcation theory, the sufficient conditions for the occurrences of transcritical bifurcation and Neimark-Sacker bifurcation and the stability of closed orbit bifurcated are obtained. Finally, the numerical simulations are presented, which not only verify the existence of Neimark-Sacker bifurcation but also reveal some new dynamic phenomena of this model.}
}