Our article “Stability of Ecological Systems: A Theoretical Review” has been published in Physics Reports. In this review, we provided a systematic and comprehensive review on the theoretical frameworks for analyzing the stability of ecological systems. Notably, we surveyed various stability notions, including linear stability, sign stability, diagonal stability, D-stability, total stability, sector stability, and structural stability. For each of these stability notions, we examined necessary or sufficient conditions for achieving such stability and demonstrate the intricate interplay of these conditions on the network structures of ecological systems. We further discussed the stability of ecological systems with higher-order interactions.
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