Periodic Fox production harvesting models with delay

L. Berezansky, L. Idels

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We investigate the behavior of population models in a periodically varying environment. In this paper, we introduce the Fox surplus harvesting model with delayfrac(d N, d t) = N (t) fenced(r (t) lnθ frac(K (t), N (g (t))) - F (t)) . We obtain explicit conditions for existence of global solutions, existence of a positive periodic solution, oscillation of all solutions about positive equilibrium and global attractivity of this equilibrium. Numerical simulations illustrate the effectiveness of the conditions for oscillations and stability of the Fox model. It was also found that oscillations in the intrinsic rate r(t) and the environmental carrying capacity K(t) contributed quantitatively and qualitatively to the system's dynamics in significant ways, and cannot be neglected in mathematical models of biological systems. Crown

Original languageEnglish
Pages (from-to)142-153
Number of pages12
JournalApplied Mathematics and Computation
Issue number1
StatePublished - 15 Jan 2008


  • Fox production models
  • Gompertzian model
  • Harvesting
  • Non-autonomous delay differential equations
  • Oscillation
  • Periodic solutions
  • Stability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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