Stability of equations with a distributed delay, monotone production and nonlinear mortality

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We consider population dynamics models dN/dt = f(N(tτ)) - d(N(t)) with an increasing fecundity function f and any mortality function d which can be quadratic, as in the logistic equation, or have a different form provided that the equation has at most one positive equilibrium. Here the delay in the production term can be distributed and unbounded. It is demonstrated that the positive equilibrium is globally attractive if it exists, otherwise all positive solutions tend to zero. Moreover, we demonstrate that solutions of the equation are intrinsically non-oscillatory: once the initial function is less/greater than the equilibrium K > 0, so is the solution for any positive time value. The assumptions on f, d and the delay are rather nonrestrictive, and several examples demonstrate that none of them can be omitted.

Original languageEnglish
Pages (from-to)2833-2849
Number of pages17
JournalNonlinearity
Volume26
Issue number10
DOIs
StatePublished - 1 Oct 2013

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy (all)
  • Applied Mathematics

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