@article{Wu2023, 
author = {Yinyin Wu and Fanfan Chen and Qingchi Ma and Dingbian Qian},
title = {Subharmonic solutions for degenerate periodic systems of Lotka-Volterra type with impulsive effects},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {9},
pages = {20080-20096},
keywords = {periodic systems of Lotka-Volterra type, subharmonic solutions, degenerate systems, impulsive effects, Poincaré-Birkhoff theorem},
url = {https://www.sciopen.com/article/10.3934/math.20231023},
doi = {10.3934/math.20231023},
abstract = {In this paper, we are concerned with the existence of subharmonic solutions for the degenerate periodic systems of Lotka-Volterra type with impulsive effects. In our degenerate model, the variation of the predator and prey populations may vanish on a time interval, which imitates the (real) possibility that the predation is seasonally absent. Our proof is based on the Poincaré-Birkhoff theorem. By using phase plane analysis, we can find the large gap in the rotation numbers between the "small" solutions and the "large" solutions, which guarantees a suitable twist property. By applying the Poincaré-Birkhoff theorem, we then obtain the existence of subharmonic solutions. Our main theorem extends the associated results by J. López-Gómez et al.}
}