Abstract
Many natural and man-made systems, from financial markets to ecosystems or the human brain, are built from multiple interconnected units. This complex high-dimensionality hinders our capacity to understand and predict the dynamics, functioning and fragility of these systems. One fragility scenario, particularly relevant to ecological communities of interacting species, concerns so-called regime shifts: abrupt and unexpected transitions from healthy, species-rich communities towards states of degraded ecosystem function and services. The accepted explanation for these shifts is that they arise as abrupt transitions between alternative stable states: multiple stable configurations of a system under the same internal and external conditions. These alternative states are well-understood in low-dimensional systems, but how they upscale with system complexity remains a debated question. In the present work we investigate the emergence of multiple stable states in a number of complex system models. We find that high-dimensional models with random interactions can unfold at least four different regimes of multistability, each emerging under a specific interaction scheme. More importantly, each multistability regime leaves a distinct and quantifiable fingerprint, providing a framework to analyze experimental evidence of abrupt shifts. By bridging previous results and studying multistability regimes, their fingerprints and their correlation with empirical evidence in ecology, our study helps define a common ground to understand and classify multiple stable states in complex systems.