15 Sept 2022
Will a large complex system be stable? Robert May asked in 1972. The answer that he provided to this question kicked off what came to be known as the complexity-stability debate. This video presents a modern review of the original paper and the perspectives that it opens up.
CONTENTS
00:00 Introduction
02:15 Stability Analysis
04:14 Jacobian Matrix
06:47 Randomness is your friend
08:50 Random matrices
13:11 May’s paradox
15:28 This changes everything
18:12 Conclusions
REFERENCES The view that “Complexity begets stability” was first challenged in numerical experiments by Gardner and Ashby [1], which May then supported by the Mathematical argument reviewed here [2]. Numerical evidence that May’s argument extends to non-stationary states was provided by Sinha and Sinha [3] [1] M.R. Gardner and W.R. Ashby: “Connectance of Large Dynamic (Cybernetic) Systems: Critical Values for Stability.” Nature 288, 784 (1970) https://doi.org/10.1038/228784a0 [2] R.M. May: Will a large complex system be stable? Nature 238, 413-414 (1972) https://doi.org/10.1038/238413a0 [3] S. Sinha and S. Sinha: “Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics.” Physical Review E 71, 020902 (2005) https://doi.org/10.1103/PhysRevE.71.0… SOURCES – The photograph “Rainforest surrounded by fog” (1:04) is the work of David Riaño Cortés and is used under a creative commons licence via Pexels. It can be found at: https://www.pexels.com/photo/rainfore… – The photograph “Photo of green field near mountains” is the work of Tim Mossholder and is used under a creative commons license via Pexels. It can be found at: https://www.pexels.com/photo/photo-of… – May’s paper (shown at 2:14) is owned by Springer Nature publishing, it is reproduced here for the purpose of review and criticism. (see References for link)
May’s Paradox – YouTube
From the channel Complexity Papers https://www.youtube.com/@complexitypapers
A channel on the mathematics of complex systems, featuring dynamics, networks, game theory, and such things. All content is produced by Thilo Gross. Thilo is professor for biodiversity theory at HIFMB. HIFMB is a collaboration of the Alfred-Wegener Institute, Helmholtz Center for Polar and Marine Research, and the Carl-von-Ossietzky University of Oldenburg. All opinions expressed in the videos are Thilo’s alone and don’t reflect positions of the institutions mentioned above.
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