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Part of the book series: NATO ASI Series ((ASIC,volume 246))

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Abstract

Numerical experiments allow the study of the local stability of dynamical systems as a function of their connectance: when this connectance is high, this local stability is improbable. Effects of substitutability versus complementarity are also studied. Moreover, as shown by the diagonal dominance theorem, the situation is quite different for some systems resulting from economic models.

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References

  1. M.R. Gardner, W.R. Ashby, “Connectance of Large Dynamic (Cybernetic) Systems: Critical Values for Stability”, Nature Vol.228,p.784, 1970.

    Article  ADS  Google Scholar 

  2. D.D. Siljak, “Large Scale Dynamic Systems. Stability and Structure”, North Holland, New York, U.S.A., 1978.

    MATH  Google Scholar 

  3. R.M. May, “Will a large complex system be stable?”, Nature, Vol.238, p.413,1972. “Stability and complexity in Model Ecosystems”, Princeton, New Jersey, Princeton University Press, U.S.A., 1974, 2nd ed.

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  4. C. Froeschle, “Connectance of Dynamical Systems with increasing number of degrees of freedom”, Phys. Rev. A, Vol.18, pp 27–281, 1 July 1978.

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  5. M. McManus, “The Arrow and Hurwicz and Hahn Theorem”, Palo Alto (Calif.), unpublished, c.f. J. Quirk and R. Saposnik, “Théorie de l’équilibre général et économie du bien-être”, p.184, Paris, PUF,1974.

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  6. C. Froeschle and A. Longhi, “Connectance et stabilité locale d’un équilibre général”, Economie appliquée, XL, 1987.

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  7. A.E.Roy, I.W. Walker and A.J.C. McDonald, “Studies in the stability of hierarchical dynamical systems” in “Stability of the solar system and its minor natural and artificial bodies”, NATO ASI Series edited by-V.G. Szebehely

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© 1988 Kluwer Academic Publishers

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Froeschlé, C., Gautero, J.L. (1988). Connectance and Stability of Linear Differential Systems. In: Roy, A.E. (eds) Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems. NATO ASI Series, vol 246. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3053-7_37

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  • DOI: https://doi.org/10.1007/978-94-009-3053-7_37

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7873-3

  • Online ISBN: 978-94-009-3053-7

  • eBook Packages: Springer Book Archive

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