Analytical solutions to a generalized growth equation

Eberhard O. Voit, Michael A. Savageau

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

Systems of the form x ̇i = αi Π n j=1Xgij j - βi Π n j=1Xhij ji = 1,...,n occur in the analysis of biological networks. They also include as special cases the known growth laws and probability functions, famous differential equations like those of Bessel, Chebyshev, and Laguerre, and solutions to important physical problems. These systems have no known analytical solution. However, an important subclass comprising many of the special cases mentioned above is solved.

Original languageEnglish (US)
Pages (from-to)380-386
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume103
Issue number2
DOIs
StatePublished - Oct 30 1984
Externally publishedYes

Fingerprint

Analytical Solution
Differential equations
Probability function
Biological Networks
Friedrich Wilhelm Bessel
Chebyshev
Differential equation
Form

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Analytical solutions to a generalized growth equation. / Voit, Eberhard O.; Savageau, Michael A.

In: Journal of Mathematical Analysis and Applications, Vol. 103, No. 2, 30.10.1984, p. 380-386.

Research output: Contribution to journalArticle

Voit, Eberhard O. ; Savageau, Michael A. / Analytical solutions to a generalized growth equation. In: Journal of Mathematical Analysis and Applications. 1984 ; Vol. 103, No. 2. pp. 380-386.
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