title: A mathematical model with pulse effect for three populations of the giant panda and two kinds of bamboo.
abstract: A mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floquet theory and comparison techniques of impulsive equations, we find conditions for the local and global stabilities of the giant panda-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent. The results provide a theoretical basis for giant panda habitat protection.
authors.affiliation: College of Forestry, Beijing Forestry University, Beijing 100083, China ; College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan, 464000, China.
authors.forename: Xiang-yun
authors.initials: XY
authors.lastname: Shi
authors.affiliation: College of Forestry, Beijing Forestry University, Beijing 100083, China ; School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China.
authors.forename: Guo-hua
authors.initials: GH
authors.lastname: Song
mesh_terms: D000824:Animal Nutritional Physiological Phenomena; D000818:Animals; D004032:Diet / Q000662:veterinary; D004463:Ecology; D017753:Ecosystem; D008962:Models, Theoretical; D009751:Nutritional Requirements; D031787:Sasa / Q000502:physiology*; D013997:Time Factors; D001503:Ursidae