One-dimensional discrete-time population models are often used to investigate the potential effects of increasing harvesting on population dynamics, and it is well known that suitable harvesting rates can stabilize fluctuations of population abundance. However, destabilization is also a possible outcome of increasing harvesting even in simple models. We provide a rigorous approach to study when harvesting is stabilizing or destabilizing, considering proportional harvesting and constant quota harvesting, that are usual strategies for the management of exploited populations. We apply our results to some of the most popular discrete-time population models (quadratic, Ricker and Bellows maps). While the usual case is that increasing harvesting is stabilizing, we prove, somehow surprisingly, that increasing values of constant harvesting can destabilize a globally stable positive equilibrium in some cases; moreover, we give a general result which ensures that global stability can be shifted to observable chaotic dynamics by increasing one model parameter, and apply this result to some of the considered harvesting models.

一维离散时间种群模型通常用于研究增加捕捞对种群动态的潜在影响，众所周知，合适的捕捞率可以稳定种群丰度的波动。然而，即使在简单的模型中，不稳定也是增加收获的可能结果。我们提供了一种严格的方法来研究何时收割是稳定或不稳定的，考虑到按比例收割和恒定配额收割，这是管理被剥削人口的常用策略。我们将我们的结果应用于一些最流行的离散时间人口模型（二次、Ricker 和 Bellows 地图）。虽然通常的情况是增加收获正在稳定，但我们以某种方式令人惊讶地证明，在某些情况下，不断增加的收获值可能会破坏全球稳定的正平衡；此外，我们给出了一个一般结果，通过增加一个模型参数，确保全局稳定性可以转变为可观察的混沌动力学，并将这一结果应用于一些考虑的收获模型。