Bulletin of Mathematical Biology

, Volume 44, Issue 1, pp 103–117 | Cite as

Random ecological systems with structure: Stability-complexity relationship

  • M. I. Granero-Porati
  • R. Kron-Morelli
  • A. Porati
Article

Abstract

We have numerically examined more than one million Large Complex Systems (LCS) of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations (GLV), with self-regulation term. The scope was to have some insight on the stability-complexity relationship.

We considered systems of prey-predator type, and we gave appropriate rules for constructing the model systems, rules that specify the behaviour of model systems in order to put them near the biological reality.

The results show, among other things, a strict correlation between the stability and the prey-predator ratio (which, in our model, uniquely determines the connectedness of the system).

Keywords

Feasible System Large Complex System Feasible Sample Absurd Situation International Cooperative Publ 

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Literature

  1. Gardner, M. R. and W. R. Ashby. 1970. “Connectedness of Large Dynamical (Cybernetic) Systems: Critical Values for Stability.”Nature,228, 784.CrossRefGoogle Scholar
  2. Gilpin, M. E. 1975. “Stability of Feasible Predator-Prey Systems.”Nature,254, 137–139.CrossRefGoogle Scholar
  3. Goel, N. S., S. C. Maitra and E. W. Montroll, 1971. “On the Volterra and other Non-Linear Models of Interacting Populations.”Rev. Mod. Phys.,43, 231–276.MathSciNetCrossRefGoogle Scholar
  4. Granero-Porati, M. I., A. Porati and A. Vecli. 1978. “Analytical Conditions for the Conservative Form of the Ecological Equations.”Bull. Math. Biol.,40, 257–264.MathSciNetCrossRefGoogle Scholar
  5. —, R. Kron-Morelli and A. Porati. 1981. “Stability of Model Systems Describing Prey-Predator Communities.” InQuantitative Population Dynamics Vol. 13. Eds. D. G. Chapman, V. Gallucci and F. M. Williams. Fairland, MD: International Cooperative Publ.Google Scholar
  6. Harary, F. 1967. “Graphical Enumeration Problems.” InGraph Theory and Theoretical Physics, New York: Academic Press.Google Scholar
  7. — 1974. “A Survey of Generalized Ramsey Theory.” InLecture Notes in Mathematics, Vol. 406, pp. 10–17, Berlin: Springer.Google Scholar
  8. May, M. R. 1972. “Will a Large Complex System be Stable?”,Nature,238, 413–414.CrossRefGoogle Scholar
  9. Roberts, A. 1974. “The Stability of Feasible Random Ecosystem.”Nature,251, 607–608.CrossRefGoogle Scholar
  10. Siljak, D. D. 1974. “Connective Stability of Complex Ecosystems.”Nature,249, 280.CrossRefGoogle Scholar
  11. — 1975. “When is a Complex-Ecosystem Stable?”Math. Biosc.,25, 25–50.MATHMathSciNetCrossRefGoogle Scholar
  12. — 1978. “Large-Scale Dynamic Systems,” New York: North Holland.Google Scholar
  13. Tregonning, K. and A. Roberts 1978. “Ecosystem-Like Behaviour of a Random-Interaction Model—I.”Bull. Math. Biol.,40, 513–524.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1982

Authors and Affiliations

  • M. I. Granero-Porati
    • 1
  • R. Kron-Morelli
    • 1
  • A. Porati
    • 1
  1. 1.Institute of Physics, Section of Biophysics, GNCB-CNRUniversity of ParmaParmaItaly

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