作为传统延拓和分岔分析补充的全局延拓
Global continuation as a complement to traditional continuation and bifurcation analysis
AI总结：
针对多稳态动力系统传统局部延拓分析的局限，本文引入全局延拓，通过整合全状态空间信息并行延续系统吸引子及其对有限扰动的响应，无需深厚专业知识，展示独特优势并开源实现，为相关研究提供新方法。
AI中文摘要：
多稳态动力系统普遍存在，用于模拟生态系统、电网、气候要素、神经元等。传统上通过分岔图分析这些系统，即局部延拓，它只能捕捉线性（局部）系统对无穷小扰动的响应，存在局限性。本文引入全局延拓作为补充，它通过整合整个状态空间的信息，并行找到并延续所有系统吸引子及其对有限扰动的响应，关注实际中从业者关心的动力学系统特性或可观测量。全局延拓无需深厚专业知识，易于使用和排查故障，通过大量示例展示了其独特优势，还以开源软件形式实现，提高了可及性。
英文摘要：
Multistable dynamical systems are ever-prevalent, used to model for example ecosystems, power grids, climate elements, neurons, and more. When perturbed, such systems may ``tip'' from one state of operation to another, often with abrupt, irreversible, and high-impact consequences in each context. Traditionally, these systems are analysed via bifurcation diagrams, the result of a process we refer to as \emph{local continuation}, as it only captures the linear (local) system response to infinitesimal perturbations. Local continuation requires substantial expertise, constant interventions, and may yield inaccurate assessment of the system's response to large perturbations that is crucial for tipping analysis. To address some inherent challenges of local continuation and to provide fundamentally new information during a continuation, this paper introduces \emph{global continuation} as a complement suitable for the study of multistability, critical transitions and real-world-oriented applications. Global continuation finds and continues in parallel (practically) all system attractors and their response to finite perturbations by synthesising information from the whole state space, while placing a focus on the qualities or observables of a dynamical system that the practitioner cares about in context. Global continuation does not require deep expertise and is effortless to use and troubleshoot, making it attractive to applied scientists from different disciplines. We highlight several unique advantages that allow global continuation to complement the status quo and exemplify them through a plethora of representative examples. Global continuation is also implemented as open source software in DynamicalSystems.jl, enhancing its accessibility.
