一类捕食-食饵模型正平衡解的整体分歧

GLOBAL BIFURCATION OF POSITIVE STEADY-STATE SOLUTIONS FOR A CLASS OF PREDATOR-PREY MODEL

讨论了一类改进的Leslie-Gower和Holling-TypeⅡ型捕食-食饵模型对应的平衡态系统正解的结构.以捕食者的出生率b为分歧参数,利用局部分歧理论和整体分歧理论,得到了此平衡态系统正解的存在性与参数b的关系,即当b适当大时,该平衡态系统具有共存正解.

In this paper the structure of a predator-prey model with modified Leslie- Gower and Holling-Type Ⅱ schemes is investigated. By use of the theorems of local bifurcation and global bifurcation theory, we get the ralationship between the existence of positive solutions for the system and bifurcation parameter b-the birth-rate of predator v, that is, the system has coexistence positive solutions when b is in a proper range.