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Differential Equations and Dynamical Systems

, Volume 27, Issue 4, pp 357–367 | Cite as

Periodic Solutions of a Nonautonomous Leslie-Gower Predator-Prey Model with Non-Linear Type Prey Harvesting on Time Scales

  • Sultan Alam
  • Syed AbbasEmail author
  • Juan J. Nieto
Original Research
  • 419 Downloads

Abstract

In this paper, we investigate the existence of periodic solutions of modified version of the Leslie-Gower predator-prey model with Holling-type II functional response in the presence of Michaelis-Menten type prey harvesting over a time scale. Sufficient conditions for the existence of periodic solutions are derived by using the continuation theorem of coincidence degree theory. The condition we obtain is easily verifiable and not much restricted.

Keywords

Prey-predator model Periodic solution Continuation theorem Coincidence degree Time scale 

Mathematics Subject Classification

34N05 34C25 92A15 47H11 

Notes

Acknowledgments

We are thankful to the anonymous reviewers for their valuable comments and suggestions which help us to improve the manuscript considerably. This work was supported by project “NBHM / IITMANDI / 2013 / NBHM / SYA / 45 / 02” National Board of Higher Mathematic, Government of India, and partially supported by the Ministerio de Economia y Competitividad of Spain under Grant MTM2013-43014-P, XUNTA under grant R2014/002, and co-financed by the European Community fund FEDER.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2015

Authors and Affiliations

  1. 1.School of Basic SciencesIndian Institute of Technology MandiMandiIndia
  2. 2.Department of Mathematical AnalysisUniversity of Santiago de CompostelaSantiago de CompostelaSpain
  3. 3.Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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