May's Paradox
Channel: Complexity Papers
Date: 2022-09-15

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.71.020902
 
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/rainforest-surrounded-by-fog-975771/
- 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-green-field-near-mountains-974314/
- 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)