Skip to main content
SpringerLink
Log in

Dynamical aspects of kinetics

  • Published:
The bulletin of mathematical biophysics Aims and scope Submit manuscript

Abstract

It is shown when and how, and with what advantage, systems of first-order differential equations of the typex i =X i (x 1,...,x n occurring so frequently in biological and chemical kinetic problems and in other places, may be made to stem from a least-action type of variational principle. Linear systems are treated in some detail, and certain aspects of Volterra's ecological kinetics and of chemical kinetics are discussed. Finally, the general conditions are elaborated under which Gibbs ensemble theory may be used in considering systems with large numbers of degrees of freedom from a statistical point of view.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Chance, B., D. Garfinkel, J. Higgins, and B. Hess. 1960. “Metabolic Control Mechanisms”.Jour. Biol. Chem.,235, 2426–2439.

    Google Scholar 

  • Feynman, R. P. 1951. “An Operator Calculus Having Applications in Quantum Electrodynamics”.Physical Review,84, 108–128.

    Article  MATH  MathSciNet  Google Scholar 

  • Fukuda, N. and M. Sugita. 1961. “Mathematical Analysis of Metabolism using an Analogue Computer”.Jour. Theoret. Biol.,1, 440–451.

    Google Scholar 

  • Hill, E. L. 1951. “Hamilton's Principle and the Conservation Theorems of Mathematical Physics”.Rev. Mod. Phy.,23, 253–260.

    Article  MATH  Google Scholar 

  • Kendall, D. G. 1949. “Stochastic Processes and Population Growth”.Jour. Roy. Statist. Soc., B. 11, 230–264.

    MATH  MathSciNet  Google Scholar 

  • Kerner, E. H. 1958. “Note on the Forced and Damped Oscillator in Quantum Mechanics”.Can. Jour. Phy.,36, 371–377.

    MATH  Google Scholar 

  • — 1959. “Further Considerations on the Statistical Mechanics of Biological Associations”.Bull. Math. Biophysics,21, 217–255.

    Article  MathSciNet  Google Scholar 

  • Lotka, A. J. 1922. “Contribution to the Energetics of Evolution”.Proc. Nat. Acad. Sci.,8, 147–154.

    Article  Google Scholar 

  • Moore, M. J. 1949. “Kinetics of Open Reaction Systems”.Trans. Far. Soc.,45, 1098–1109.

    Article  Google Scholar 

  • Wedderburn, J. H. M. 1934.Lectures on Matrices. New York: Amer. Math. Soc.

    Google Scholar 

  • Whittaker, E. T. 1937.Analytical Dynamics. Cambridge: University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Delaware, Newark, Delaware

    Edward H. Kerner

Authors
  1. Edward H. Kerner
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kerner, E.H. Dynamical aspects of kinetics. Bulletin of Mathematical Biophysics 26, 333–349 (1964). https://doi.org/10.1007/BF02484234

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02484234

Keywords

Search

Navigation