一类具有恐惧效应的时滞食物链模型周期解

Periodic solutions of a delayed food chain model with fear effect

研究了一类具有恐惧效应的时滞食物链模型.以食饵种群和中层捕食者种群感受到被捕食危机时的反应时间时滞为分岔参数,讨论了模型Hopf分岔的存在性.利用中心流形定理和规范型理论研究了模型分岔周期解的性质,利用仿真示例验证了所得结果的正确性.

A three-species food chain model with time delay and fear effect was investigated.The existence of Hopf bifurcation of the model was discussed by taking the time delay due to the reaction time of the prey species and the middle predator species when they felt the predation crisis as bifurcation parameter.Furthermore,properties of bifurcating periodic solutions were studied by using the center manifold theorem and normal form theory.Finally,a numerical example was presented tosubstantiate the obtained analytical results.