Persistence and propagation of species are fundamental questions in spatial ecology. This paper focuses on the impact of Allee effect on the persistence and propagation of a population with birth pulse. We investigate the threshold dynamics of an impulsive reaction–diffusion model and provide the existence of bistable traveling waves connecting two stable equilibria. To prove the existence of bistable waves, we extend the method of monotone semiflows to impulsive reaction–diffusion systems. We use the methods of upper and lower solutions and the convergence theorem for monotone semiflows to prove the global stability of traveling waves and their uniqueness up to translation. Then we enhance the stability of bistable traveling waves to global exponential stability. Numerical simulations illustrate our theoretical results.

物种的持久性和繁殖是空间生态学的基本问题。本文重点研究Allee效应对具有出生脉冲的人群的持续性和繁殖的影响。我们研究了脉冲反应扩散模型的阈值动力学，并提供了连接两个稳定平衡的双稳态行波的存在。为了证明双稳态波的存在，我们将单调半流方法扩展到脉冲反应扩散系统。我们使用上下解的方法以及单调半流的收敛定理来证明行波的整体稳定性及其在平移之前的唯一性。然后，我们将双稳态行波的稳定性提高到全局指数稳定性。数值模拟说明了我们的理论结果。