Assessing and managing the human influence on the natural and anthropic ecosystems strongly demands for robust measures of their resilience, especially in a world facing global changes as it is the Earth now. Many definitions of resilience have been proposed in order to cover different contexts. However, they are mostly derived either from the ecological or the engineering definitions of resilience, which substantially differ between each other. Here, following the strategy for measuring the system perturbations by the return period of their impacts on production (or equivalently by the inverse frequency), I demonstrate the mathematical equivalence of the ecological and engineering definitions of resilience for a special class of production systems. These finding provides additional robustness to resilience assessments based on the recently proposed annual production resilience indicator.

中文翻译：

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协调弹性的生态和工程定义

评估和管理人类对自然和人类生态系统的影响强烈要求采取强有力的措施来增强其弹性，特别是在当今地球正面临全球变化的世界中。为了涵盖不同的环境，已经提出了许多弹性的定义。但是，它们主要是从弹性的生态学定义或工程学定义衍生而来的，两者之间存在很大差异。在这里，按照通过对生产的影响的恢复期来衡量系统扰动的策略（或等效地通过逆频率），我展示了特殊生产系统的弹性的生态学和工程学定义的数学等价性。