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A stage-structured predator-prey system with time delay

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Abstract

A stage-structured predator-prey system with time delay is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, China

    Lingshu Wang, Rui Xu & Guanghui Feng

  2. School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang, 050061, China

    Lingshu Wang

Authors
  1. Lingshu Wang
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  2. Rui Xu
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  3. Guanghui Feng
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Corresponding author

Correspondence to Lingshu Wang.

Additional information

R. Xu was supported by the National Natural Science Foundation of China (No. 10671209), China Postdoctoral Science Foundation (No. 20060391010), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

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Wang, L., Xu, R. & Feng, G. A stage-structured predator-prey system with time delay. J. Appl. Math. Comput. 33, 267–281 (2010). https://doi.org/10.1007/s12190-009-0286-x

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  • DOI: https://doi.org/10.1007/s12190-009-0286-x

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