Multiperiodicity to a Certain Delayed Predator–Prey Model

Abstract

The delayed predator–prey system with generalized non-monotonic functional responses and stage structure was investigated in the present paper. By virtue of Mawhin’s coincidence degree and the application of inequalities technique, we are successful to generate some novel conditions to guarantee that the system has at least two positive periodic solutions. It is shown that all parameters of the system have effects on the existence of positive periodic solutions and the period of the coefficients can also affect the existence of positive periodic solutions. In the end, an illustrative example is presented to the feasibility of the main results.

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Acknowledgements

The authors would like to thank the editors and anonymous reviewers for their constructive suggestions towards upgrading the quality of the manuscript.

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Correspondence to Xiang-Lai Zhuo.

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This work is supported by the National Natural Science Foundation of China (60672085, 51804179), Natural Foundation of Shandong Province (ZR2016EEB07) and the Reform of Undergraduate Education in Shandong Province Research Projects (2015M139)

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Cite this article

Li, Y., Zhuo, X. & Zhang, F. Multiperiodicity to a Certain Delayed Predator–Prey Model. Qual. Theory Dyn. Syst. 18, 793–811 (2019). https://doi.org/10.1007/s12346-018-00313-5

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Keywords

  • Multiperiodicity
  • Predator–prey model
  • Stage structure
  • Generalized non-monotone functional response

Mathematics Subject Classification

  • 34C25
  • 92B05