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Differential Equations and Dynamical Systems

, Volume 27, Issue 4, pp 439–447 | Cite as

Necessary and Sufficient Conditions for the Existence of Periodic Solutions of a Nicholson Type Delay System

  • Pablo AmsterEmail author
  • Alberto Déboli
Original Research
  • 73 Downloads

Abstract

We consider a Nicholson type system for two species with mutualism and nonlinear harvesting terms. We give sufficient conditions for the existence of a positive periodic solution. We also provide a necessary condition; more precisely, we prove that if the harvesting rate is large enough, then 0 is a global attractor for the positive solutions and, in particular, positive periodic solutions cannot exist.

Keywords

Nicholson type system Nonlinear harvesting Delay differential systems Positive periodic solutions Topological degree 

Mathematics Subject Classification

34K13 92D25 

Notes

Acknowledgments

The authors thank the referees for the careful reading of the manuscript and the fruitful corrections and remarks. This work was partially supported by project UBACyT 20020120100029BA.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2016

Authors and Affiliations

  1. 1.Departamento de Matemática-FCEyNUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.IMAS-CONICETCiudad UniversitariaBuenos AiresArgentina

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