Journal of Dynamics and Differential Equations

, Volume 26, Issue 3, pp 723–744 | Cite as

Persistence, Permanence and Global Stability for an \(n\)-Dimensional Nicholson System

  • Teresa FariaEmail author
  • Gergely Röst


For a Nicholson’s blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.


Nicholson’s blowflies equation Delays Persistence Permanence Global asymptotic stability 

Mathematics Subject Classification (2010 )

34K20 34K25 34K12 92D25 



Work supported by Fundação para a Ciência e a Tecnologia, PEst-OE/MAT/UI0209/2011 (T. Faria) and by ERC Starting Grant Nr. 259559, OTKA K109782 and ESF project (TÁMOP-4.2.2.C-11/1/KONV-2012-0013) (G. Röst).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Departamento de Matemática and CMAF, Faculdade de CiênciasUniversidade de Lisboa, Campo GrandeLisboaPortugal
  2. 2.Bolyai InstituteUniversity of SzegedSzegedHungary

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