A considerable amount of analytical work has been done in recent years to understand extinction in finite discrete population systems in the presence of demographic noise. This has been made possible by advances in employing the WKB method for solving a wide variety of stochastic single population systems. Previous works have focussed on extinction in logistic/Verhulst-type models with a single stable fixed point, Allee-type models which has an additional unstable nonzero fixed point and switching behaviour of bistable finite population systems. However, the mean extinction time in bistable systems with an absorbing state hasn’t received much focus in these studies. In this work, we study the mean extinction time (MTE) in a phenomenological single population model exhibiting bistability using the WKB method. The quasi-stationary distribution (QSD) is derived in the limit of a large parameter, N, of the model, and by matching the QSD in different regimes of stability, an analytical expression for the mean extinction time has been derived. The MTE is exponentially large in N but shows a significant reduction in the extinction time due to the presence of bistable fixed points as compared to models that have only single stable states such as the Verhulst model. It is demonstrated that the analytical results compare well with that derived from direct numerical calculations.

近年来，为了理解存在人口噪声的有限离散种群系统中的灭绝，已经进行了大量的分析工作。通过使用 WKB 方法解决各种随机单一种群系统的进步，这已成为可能。以前的工作集中在具有单个稳定不动点的逻辑/Verhulst 型模型中的灭绝，Allee 型模型具有额外的不稳定非零不动点和双稳态有限种群系统的切换行为。然而，在这些研究中，具有吸收状态的双稳态系统的平均消光时间并没有得到太多关注。在这项工作中，我们使用 WKB 方法研究了表现出双稳定性的现象学单一种群模型中的平均消光时间 (MTE)。N，通过匹配不同稳定状态下的 QSD，推导出平均消光时间的解析表达式。MTE 在N 中呈指数级大，但与 Verhulst 模型等只有单一稳定状态的模型相比，由于双稳态不动点的存在，消光时间显着减少。结果表明，分析结果与直接数值计算得出的结果相比很好。