Complex adaptive systems (CASs), from ecosystems to economies, are open systems and inherently dependent on external conditions. While a system can transition from one state to another based on the magnitude of change in external conditions, the rate of change -- irrespective of magnitude -- may also lead to system state changes due to a phenomenon known as a rate-induced transition (RIT). This study presents a novel framework that captures RITs in CASs through a local model and a network extension where each node contributes to the structural adaptability of others. Our findings reveal how RITs occur at a critical environmental change rate, with lower-degree nodes tipping first due to fewer connections and reduced adaptive capacity. High-degree nodes tip later as their adaptability sources (lower-degree nodes) collapse. This pattern persists across various network structures. Our study calls for an extended perspective when managing CASs, emphasizing the need to focus not only on thresholds of external conditions but also the rate at which those conditions change, particularly in the context of the collapse of surrounding systems that contribute to the focal system's resilience. Our analytical method opens a path to designing management policies that mitigate RIT impacts and enhance resilience in ecological, social, and socioecological systems. These policies could include controlling environmental change rates, fostering system adaptability, implementing adaptive management strategies, and building capacity and knowledge exchange. Our study contributes to the understanding of RIT dynamics and informs effective management strategies for complex adaptive systems in the face of rapid environmental change.

翻译：复杂适应系统（CASs），从生态系统到经济系统，均为开放系统，本质上依赖外部条件。虽然系统可能因外部条件变化的幅度而从一种状态转变为另一种状态，但变化速率——不论幅度大小——也可能因一种被称为速率诱导转变（RIT）的现象导致系统状态改变。本研究提出一个新颖框架，通过局部模型及网络扩展（其中每个节点为其他节点提供结构适应性）来捕捉CASs中的RITs。我们的发现揭示了RITs如何在关键环境变化速率下发生：低度数节点因连接较少、适应能力降低而率先翻转；高度数节点随后翻转，因其适应来源（低度数节点）崩溃。这一模式在各种网络结构中持续存在。本研究呼吁在管理CASs时采用扩展视角，强调不仅需关注外部条件的阈值，更需关注这些条件变化的速率，尤其是在对焦点系统韧性有贡献的周边系统崩溃的背景下。我们的分析方法为设计管理策略开辟了路径，以缓解RIT影响并增强生态、社会及社会生态系统的韧性。这些策略可包括控制环境变化速率、培育系统适应性、实施适应性管理策略以及建设能力与知识交流。本研究有助于理解RIT动力学，并为快速环境变化下复杂适应系统的有效管理策略提供信息。