On the global attractivity for a logistic equation with piecewise constant arguments

Kazuya Uesugi, Yoshiaki Muroya, Emiko Ishiwata

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16 Citations (Scopus)

Abstract

In this paper, we consider the following logistic equation with piecewise constant arguments: {dN(t)/dt=rN(t){1-∑j=0 majN([t-j])}, t≥0, m≥1, N(0)=N0>0, N(-j)=N-j≥0, j=1,2,...,m, where r>0, a0,a1, ...,am≥0, ∑j=0 m aj>0, and [x] means the maximal integer not greater than x. The sequence {Nn}n=0 , where Nn=N(n), n=0,1,2,... satisfies the difference equation Nn+1=Nnexp{ r(1-∑j=0 m aj Nn-j n=0,1,2,.... Under the condition that the first term a0 dominates the other m coefficient s ai, 1≤i≤m, we establish new sufficient conditions of the global asymptotic stability for the positive equilibrium N*= 1/(∑j=0 maj).

Original languageEnglish
Pages (from-to)560-580
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume294
Issue number2
DOIs
Publication statusPublished - 15 Jun 2004

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Keywords

  • Global attractivity
  • Logistic equation
  • Piecewise constant arguments

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