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恐惧效应下具有时滞的捕食–食饵模型中的动力学影响
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Abstract:
为了研究恐惧效应与时滞对生态学的影响，建立了一类具有恐惧效应的时滞捕食–食饵模型。其中捕食者被寄生虫感染且不具备免疫能力。本文首先分析解的非负性和有界性；其次，将捕食者种群的时滞响应作为分支参数，研究时滞对该模型正平衡点稳定性的影响，得到了产生Hopf分支的条件。利用数值模拟得到不同情况下的时间序列图证明了时滞对捕食–食饵模型的影响。
To investigate the impact of time delay on the dynamic behavior between prey and predator with a fear effect and a bilinear incidence rate, a class of delayed predator-prey models with a fear effect is established. In this model, the predator is infected with parasites and lacks immunity. This paper first analyzes the positive invariant set of the solution; secondly, considering the time delay response of the predator population as a bifurcation parameter, the effect of the time delay on the stability of the positive equilibrium point of the model is studied, and the conditions for Hopf bifurcation are obtained. Numerical simulations of time series diagrams under different conditions are used to demonstrate the impact of time delay on the predator-prey model.
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