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Stability and Hopf bifurcation in a three-species system with feedback delays

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Abstract

A kind of three-species system with Holling type II functional response and feedback delays is introduced. By analyzing the associated characteristic equation, its local stability and the existence of Hopf bifurcation are obtained. We derive explicit formulas to determine the direction of the Hopf bifurcation and the stability of periodic solution bifurcated out by using the normal-form method and center manifold theorem. Numerical simulations confirm our theoretical findings.

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Authors and Affiliations

  1. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People’s Republic of China

    Xin-You Meng, Hai-Feng Huo, Xiao-Bing Zhang & Hong Xiang

Authors
  1. Xin-You Meng
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  2. Hai-Feng Huo
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  3. Xiao-Bing Zhang
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  4. Hong Xiang
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Corresponding author

Correspondence to Hai-Feng Huo.

Additional information

This work was partially supported by the NNSF of China (10961018), the Key Project of Chinese Ministry of Education (209131), The Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, the NSF of Bureau of Education of Gansu Province of China (0803-01) and the Development Program for Outstanding Young Teachers in Lanzhou University of Technology (Q200703) and the Doctor’s Foundation of Lanzhou University of Technology.

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Meng, XY., Huo, HF., Zhang, XB. et al. Stability and Hopf bifurcation in a three-species system with feedback delays. Nonlinear Dyn 64, 349–364 (2011). https://doi.org/10.1007/s11071-010-9866-4

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  • DOI: https://doi.org/10.1007/s11071-010-9866-4

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