Abstract
Gardner and Ashby1 have studied the relation between the probability of stability p(S) and the extent of connectedness (“connectance”) C of large linear dynamical systems. They found a very interesting on–off-type (numerical) result: for reasonably large systems (number of components n ≥ 10) there is a critical value, Cc of C, below which the system is almost certainly stable, but above which it becomes almost certainly unstable.
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References
Gardner, M. R., and Ashby, W. R., Nature, 228, 784 (1970).
Gantmacher, F. R., Applications of the Theory of Matrices, ch. v (Interscience, New York, 1959).
Minorsky, N., Theory of Nonlinear Control Systems, ch. 4 (McGraw-Hill, New York, 1969).
Kauffman, S. A., J. Theoret. Biol., 22, 437 (1969).
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SOMORJAI, R., GOSWAMI, D. Relationship between Stability and Connectedness of Non-linear Systems. Nature 236, 466 (1972). https://doi.org/10.1038/236466a0
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DOI: https://doi.org/10.1038/236466a0
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