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

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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.

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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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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175001, H. P., India

    Sultan Alam & Syed Abbas

  2. Department of Mathematical Analysis, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

  3. Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia

    Juan J. Nieto

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  1. Sultan Alam
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  2. Syed Abbas
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  3. Juan J. Nieto
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Correspondence to Syed Abbas.

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Alam, S., Abbas, S. & Nieto, J.J. Periodic Solutions of a Nonautonomous Leslie-Gower Predator-Prey Model with Non-Linear Type Prey Harvesting on Time Scales. Differ Equ Dyn Syst 27, 357–367 (2019). https://doi.org/10.1007/s12591-015-0267-5

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  • DOI: https://doi.org/10.1007/s12591-015-0267-5

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