A Framework to Use Bifurcation Analysis for Insight into Complex Systems Resilience

Abstract

The increasing complexity and integration of systems present challenges in understanding and managing these systems, as highlighted by the INCOSE Systems Engineering Vision for 2035. This complexity risks system failures due to insufficient understanding. Resilience Engineering is a field that focuses on system behavior in the face of disruptions. However, existing methods to measure resilience, such as probability‐based measures and linear recovery models, are limited by the non‐linear and dynamic nature of modern systems. Bifurcation Analysis, a mathematical system dynamics technique, offers a different perspective by examining how systems behave under changing conditions. This approach, developed in ecology and traditionally applied in fields including power systems and neural networks, can provide insights into the resilient characteristics of non‐linear systems. Despite its promise, Bifurcation Analysis is not usually associated with Resilience Engineering. This paper proposes using Bifurcation Analysis to understand system resilience better and support Resilience Engineering practitioners. It aims to bridge the gap between the two fields, offering a framework for integrating both approaches. This framework is then applied to a model system to demonstrate its potential to enhance the understanding of system resilience. Contributions are an overview of current Resilience Engineering and Bifurcation Analysis, a general‐use framework for practitioners, and an application of this framework. Future work will focus on applying the new framework to more cases, allowing for improved Resilience Engineering, and improving the framework to make it more accessible, versatile, and reliable.