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

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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.

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References

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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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Authors and Affiliations

  1. Departamento de Matemática-FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina

    Pablo Amster & Alberto Déboli

  2. IMAS-CONICET, Ciudad Universitaria, Pab. I, 1428, Buenos Aires, Argentina

    Pablo Amster

Authors
  1. Pablo Amster
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  2. Alberto Déboli
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Correspondence to Pablo Amster.

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Amster, P., Déboli, A. Necessary and Sufficient Conditions for the Existence of Periodic Solutions of a Nicholson Type Delay System. Differ Equ Dyn Syst 27, 439–447 (2019). https://doi.org/10.1007/s12591-016-0285-y

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  • DOI: https://doi.org/10.1007/s12591-016-0285-y

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