一类竞争模型正解的唯一性和多重性

摘要

A competition model with Holling type Ⅲ functional response is studied.Firstly,by calculating the fixed point index,the sufficient conditions of the existence of positive solutions are obtained.Secondly,using the linear operator perturbation theory and standard elliptic equations regularity theory, the uniqueness and global stability of positive solutions are investigated. In addition,the multiplicity of positive solutions is discussed by the combination of the global bifurcation theory and degree theory.Finally,the theoretical results obtained are verified by the numerical simulation.It is proved that the model has multiple solutions and only one unique globally attractive solution for a suitable range of parameters.%研究了一类带有 Holling Ⅲ型功能反应的竞争模型。首先通过计算不动点指标得到了正解存在的充分条件。其次运用线性算子扰动理论以及标准的椭圆方程正则性理论研究了正解的唯一性和全局稳定性。然后应用全局分歧理论和度理论考察了正解的多重性。最后用数值模拟对所得理论结果进行了验证。研究结果表明参数满足一定条件，该模型存在多重解和全局吸引的唯一解。