Bulletin of Mathematical Biology

, Volume 39, Issue 5, pp 565–575 | Cite as

Analytical theory of the control equations for protein synthesis in the Goodwin model

  • Virendra Singh
Article

Abstract

The analytical expressions, and their convergent series expansions, for the time period and various time averages of the dynamical quantities are derived for the Goodwin model. The radius of convergence of the series expansions is also calculated. The changes necessary to fully take into account the restrictions on dynamical variable, following from the positivity of physical quantities of the model, for the statistical mechanical treatment of the system are also discussed.

Keywords

Series Expansion Dynamical Variable Control Equation Dirac Delta Function Allowed Range 

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Literature

  1. Goel, N. S. S. C. Maitra and E. W. Montroll. 1971. “On the Volterra and Other Nonlinear models of Interacting Populations”.Rev. Mod. Phys.,43, 231–276.MathSciNetCrossRefGoogle Scholar
  2. Goodwin, B. C. 1963.Temporal Organization in Cells, London and New York: Academic Press.Google Scholar
  3. Pavlidis, T. 1973.Biological Oscillators: Their Mathematical Analysis, London and New York: Academic Press.Google Scholar
  4. Maynard Smith, J. 1968.Mathematical Ideas in Biology, London: Cambridge University Press.Google Scholar

Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • Virendra Singh
    • 1
  1. 1.Department of Theoretical PhysicsTata Institute of Fundamental ResearchBombayIndia

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