Mackey-glass equation with variable coefficients

L. Berezansky, E. Braverman

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

The Mackey-Glass equation, frac(d N, d t) = frac(r (t) N (g (t)), 1 + N (g (t))γ) - b (t) N (t), is considered, with variable coefficients and a nonconstant delay. Under rather natural assumptions all solutions are positive and bounded. Persistence and extinction conditions are presented for this equation. In the case when there exists a constant positive equilibrium, local asymptotic stability of the constant solution and oscillation about this equilibrium are analyzed. The results are illustrated by numerical examples. In particular, it is demonstrated that with delay in both terms, a solution with positive initial conditions may become negative.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalComputers and Mathematics with Applications
Volume51
Issue number1
DOIs
StatePublished - 1 Jan 2006

Keywords

  • Asymptotics
  • Delay equations
  • Extinction and persistence
  • Mackey-Glass equation
  • Oscillation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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