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A generalized predator–prey system with multiple discrete delays and habitat complexity

  • Zhihui MaEmail author
  • Shufan Wang
Original Paper
  • 89 Downloads

Abstract

A generalized predator–prey model with multiple discrete delays and the effect of habitat complexity is proposed in this paper. Firstly, the stability of the considered model system and existence of Hopf bifurcations are investigated by the differential equation theory. Secondly, the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations. Most importantly and interestingly, this paper gives a class of the corresponding model systems, and some published works become special cases of ours.

Keywords

Predator–prey system Discrete delay Habitat complexity Stability Hopf bifurcation 

Mathematics Subject Classification

37C75 34K18 92B05 92D25 93D20 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (no. 11301238) and the Fundamental Research Funds for the Central Universities (no. lzujbky-2017-166).

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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.School of Mathematics and Computer ScienceNorthwest University for NationalitiesLanzhouPeople’s Republic of China

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