Abstract
GARDNER and Ashby1 have given an account of the sudden onset of instability at a particular connectance in a set of N first-order linear equations, described by ẋi = Aijxj. They gave graphs for N = 4, 7 and 10, showing how the probability of stability varied with the connectivity, C, which was defined as the fraction of the coefficients Aij (i ≠ j) allowed to be non-zero. These couplings, Aij, were uniformly distributed randomly between +1.0 and −1.0, and the diagonal terms, Aii, were uniformly distributed between −0.1 and −1.0. This result seemed to be of great importance as a model for many real systems.
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References
Gardner, M. R., and Ashby, W. R., Nature, 228, 784 (1970).
Siljak, D. D., Nature, 249, 280 (1974).
May, R. M., Nature, 238, 413–414 (1972).
Somorjai, R. L., and Goswami, D. N., Nature, 236, 466 (1972).
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DANIELS, J., MACKAY, A. The stability of connected linear systems. Nature 251, 49–50 (1974). https://doi.org/10.1038/251049a0
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DOI: https://doi.org/10.1038/251049a0
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