一类具有移居常数和年龄结构的食饵-捕食模型

摘要

考虑一类食饵具有移居常数,捕食者具有年龄结构的食饵-捕食模型.首先,研究了系统的一致有界性、局部稳定性及持久性.接着,利用Lyapunov函数和LaSalle不变性原理,给出系统全局渐近稳定的充分条件.所得结论表明,当移居常数足够小时,不影响捕食者的灭绝性,而当移居常数足够大时,食饵和捕食者将长期共存.最后,通过数值模拟来说明理论结果是正确的.%A predator-prey system with prey immigration and stage structure for the predator is investigated. Firstly,the positivity, boundedness and conditions for persistence have been derived.Furthermore, by using Lyapunov functionals and the LaSalle invariance principle,sufficient conditions are derived for the global stabili-ty of the equilibrium.When the prey immigration is small enough,the prey immigration does not affect the ex-tinction of predator,and when the prey immigration is large enough,the prey and the predator will coexist.Fi-nally numerical simulations are carried out to illustrate the correctness of the main theoretical results.