Research on Bogdanov-Takens Bifurcation of a Leslie-Type Tritrophic Model with Holling II-II Functional Responses

针对一类Leslie型三种群食物链模型，分析了该模型的余维二Bogdanov-Takens分岔行为。假设猎物满足Logistic增长速率，捕食者(超级捕食者)种群通过Holling II功能反应吃掉猎物(捕食者)。首先，给出了保证系统具有正平衡点的条件，及在该正平衡点发生Bogdanov-Takens分岔的参数条件；其次，选取了满足上述条件的适当参数，对Bogdanov-Takens分岔的非退化条件及正则性条件分别进行了验证。For a class of Leslie-type three-species food chain models, the bifurcation behavior of dimension two with residual structure of Bogdanov-Takens was analyzed. Assuming that the prey follows the Logistic growth rate, the predator (superpredator) population feeds on the prey (predator) through the Holling II functional response. Firstly, the conditions ensuring the existence of a positive equilibrium point of the system and the parameter conditions for the occurrence of Bogdanov-Takens bifurcation at this equilibrium point were given; Secondly, under appropriate parameters which satisfying the above conditions, the non-degenerate conditions and regularity conditions for the Bogdanov-Takens bifurcation were verified respectively.