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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

The May-Wigner stability theorem for connected matrices


Author: Harold M. Hastings
Journal: Bull. Amer. Math. Soc. 7 (1982), 387-388
MSC (1980): Primary 15A52, 34D05, 82A99, 92A15, 92A17
MathSciNet review: 663791
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References [Enhancements On Off] (What's this?)

  • 1. Béla Bollobás, Graph theory, Graduate Texts in Mathematics, vol. 63, Springer-Verlag, New York-Berlin, 1979. An introductory course. MR 536131 (80j:05053)
  • 2. M. R. Gardner and W. R. Ashby, Connectance of large dynamic (cybernetic) systems: critical values for stability, Nature 228 (1970), 784.
  • 3. Harold M. Hastings, The May-Wigner stability theorem, J. Theoret. Biol. 97 (1982), no. 2, 155–166. MR 676770 (84c:92058), http://dx.doi.org/10.1016/0022-5193(82)90096-0
  • 4. R. M. May, Will a large complex system be stable?, Nature 238 (1972), 413-414.
  • 5. R. M. May, Stability and complexity of model ecosystems, Princeton Univ. Press, Princeton, N. J., 1974.
  • 6. M. L. Mehta, Random matrices and the statistical theory of energy levels, Academic Press, New York-London, 1967. MR 0220494 (36 #3554)
  • 7. E. P. Wigner, Statistical properties of real symmetric matrices with many dimensions, Proc. Fourth Canad. Math. Congr. (M. S. MacPhail, ed.) Univ. Toronto Press, Toronto, 1959, pp. 174-184.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1982-15045-5
PII: S 0273-0979(1982)15045-5