一类具有线性捕获和其他食物来源的捕食-食饵模型的稳定性研究

Stability of a predator-prey model with linear harvesting and additional food source

研究了一类具有线性捕获和其他食物来源的捕食-食饵模型平衡点的局部和全局稳定性,并用实例验证了所得结果的正确性.研究结果显示:当捕食者的其他食物来源较多时,会导致食饵种群绝灭;当捕食者的其他食物来源较少时,少量的捕获会保持食饵种群和捕食者种群共存,而过度捕获则会导致食饵种群的绝灭.

The local and global stability of the equilibrium points of a predator-prey model with linear harvesting and additional food source are studied.The correctness of the main conclusions are verified by numerical simulations.The results show that when the predator has more additional food source,it will lead to the extinction of the prey population;when the predator has less additional food source,the small harvesting will keep the coexistence of the prey and predator populations,but the excessive harvesting will lead to the extinction of the prey population.