Persistence and stability properties are considered for a class of forced positive nonlinear delay-differential systems which arise in mathematical ecology and other applied contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes in an ecological setting), disturbances induced by seasonal or environmental variation, or migration. We provide necessary and sufficient conditions under which the states of these models are semi-globally persistent, uniformly with respect to the initial conditions and forcing terms. Under mild assumptions, the model under consideration naturally admits two steady states (equilibria) when unforced: the origin and a unique non-zero steady state. We present sufficient conditions for the non-zero steady state to be stable in a sense which is reminiscent of input-to-state stability, a stability notion for forced systems developed in control theory. In the absence of forcing, our input-to-sate stability concept is identical to semi-global exponential stability.

对于在数学生态学和其他应用环境中出现的一类强制正非线性延迟微分系统，考虑了持久性和稳定性属性。强迫包括控制行动（例如生态环境中的收获或繁殖计划）、季节性或环境变化引起的干扰或迁移的影响。我们提供了充分必要条件，在这些条件下，这些模型的状态在初始条件和强迫项方面是半全局持久的。在温和的假设下，所考虑的模型在非受迫时自然会承认两个稳态（平衡）：原点和独特的非零稳态。我们提出了非零稳态在某种意义上稳定的充分条件，这让人想起输入到状态稳定性，这是控制理论中开发的强制系统的稳定性概念。在没有强制的情况下，我们的输入到状态稳定性概念与半全局指数稳定性相同。