Bulletin of Mathematical Biology

, Volume 45, Issue 6, pp 969–980 | Cite as

Sequential behavior and stability properties of enzymatic neuron networks

  • Roberto R. Kampfner
  • Michael Conrad


The cycle structure of enzymatic neural networks may be characterized in terms of number of cycles exhibited, size of cycle state sets and cycle lengths. Simulation experiments show that the stability properties of these networks have some unusual features which are not exhibited by networks of two-state switching elements or by randomly constructed ecosystem models. The behavioral and structural stability of these systems decreases with their structural complexity, as measured by the number of components. The behavioral and structural stability of enzymatic neural networks also decreases with structural complexity, as measured by the number of excitase types, but only up to the middle level of excitases per neuron. This is the point of highest potential responsiveness of the system to environmental stimuli. Beyond this point the behavioral and structural stability increase. This is due to the fact that the number of possible states increases up to this point and decreases beyond it. The number of possible states, not the number of components, serves as the useful measure of complexity in these types of systems. The selection circuits learning algorithm has been used to evolve networks whose cycle structures have desired features.


Structural Stability Boolean Function Cycle Length Stability Property Connect Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Gardner, M. R., and W. R. Ashby. 1970. “Connectance of Large Dynamical (Cybernetic) Systems: Critical Values for Stability.”Nature, Lond. 228, 784.CrossRefGoogle Scholar
  2. Hastings, H. M. 1982. “The May-Wigner Stability Theorem.”J. theor. Biol. 97, 155–166.MathSciNetCrossRefGoogle Scholar
  3. Kampfner, R. and M. Conrad. 1983. “Computational Modeling of Evolutionary Learning Processes in the Brain.”Bull. math. Biol. In press. Wayne State UniversityGoogle Scholar
  4. Kauffman, S. 1970. “Behavior of Randomly Constructed Genetic Nets: Binary Element Nets.” InTowards a Theoretical Biology. 3. Drafts. Ed. C. H. Waddington Chicago, IL: Aldine.Google Scholar
  5. May, R. M. 1974.Stability and Complexity in Model Ecosystems. Princeton, NJ: Princeton University Press.Google Scholar
  6. McMurtrie, R. E. 1975. “Determinants of Stability of Large, Randomly Connected Systems.”J. theor. Biol. 50, 1–11.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1983

Authors and Affiliations

  • Roberto R. Kampfner
    • 1
  • Michael Conrad
    • 1
  1. 1.Department of Computer ScienceWayne State UniversityDetroitU.S.A.

Personalised recommendations