在本文中,我们研究了弱Allee效应下不育蚊子释放技术(SIT)的两种释放策略模型,重点分析了不育蚊子的恒定释放策略和脉冲释放策略的可行性。针对恒定释放策略,我们得到了一个与野生蚊子种群灭绝相对应的边界平衡点的存在性与稳定性结果,并且探讨了代表野生蚊子和不育蚊子共存的内部平衡点的存在性和稳定性。与此同时,我们通过考察脉冲释放策略的平凡周期解存在性与稳定性以及非平凡解的存在性,进一步深入研究了脉冲释放策略的可行性。最后,数值模拟结果为在特定参数条件下存在非平凡周期解提供了有力证据,强烈显示出该系统中可能存在非平凡周期解现象。In this paper, we investigate two models of the Sterile Insect Technique (SIT) under weak Allee effect, and focus on two strategies of constant release and pulse release of sterile mosquitoes. For the constant release strategy, we establish the existence and stability of a boundary equilibrium corresponding to the extinction of wild mosquito populations, as well as an internal equilibrium representing the coexistence of both wild and sterile mosquito types. Correspondingly, we investigate the pulse release strategy by examining the existence and stability of its trivial periodic solution, as well as non-trivial solutions. Our numerical simulations provide compelling evidence for the existence of nontrivial periodic solutions under certain parameter conditions, strongly suggesting the presence of periodic solutions within the system.
