具有非常数死亡率的捕食者-食饵模型的稳定性

Stability of a Predator-Prey Model with Nonconstant Death Rate

生态学上捕食者的死亡率不是常数而是非常数。本文结合经典的捕食者-食饵模型,研究了一类捕食者具有非常数死亡率的捕食者-食饵模型,主要讨论了非负平衡点的存在性、个数以及稳定性的条件,并通过数值模拟验证了结论的可行性。结果显示,与常数死亡率相比,非常数死亡率模型正平衡点的个数增加,使得模型的生物意义增强且动力学行为更为复杂。

Ecologically,since the mortality of a predator is not a constant but an invariant number.Using the classic pred-ator-prey model,this paper studies a class of predator-prey model with an invariant mortality of a predator.In this paper,the existence,number and stability of non-negative equilibrium are discussed,and the feasibility of the conclusion is verified by numerical simulation.The results show that the number of positive equilibria increases compared with the constant mortality rate,which makes the model more biologically significant and more complex in dynamic behavior.