Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2016, Vol. 33 ›› Issue (2): 138-150.doi: 10.3969/j.issn.1005-3085.2016.02.004

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Stability Analysis on a Ratio-dependent Predator-prey Model with Time Delay and Stage Structure

WANG Ling-shu1,  ZHANG Ya-nan1,  FENG Guang-hui2   

  1. 1- School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061
    2- Department of Basic Courses, Mechanical Engineering College, Shijiazhuang 050003
  • Received:2014-03-25 Accepted:2016-01-05 Online:2016-04-15 Published:2016-06-15
  • Supported by:
    The National Natural Science Foundation of China (11101117); the Scientific Research Foundation of Hebei Education Department (QN2014040); the Foundation of Hebei University of Economics & Business (2015KYQ01).

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Abstract:

In this paper, a ratio-dependent predator-prey model with time delay due to the gestation of the predator and stage structure for both the predator and the prey is investigated. By analyzing the characteristic equations and applying Hurwitz criterion, the local stability of a semi-trivial boundary equilibrium and a positive equilibrium are discussed, respectively. Moreover, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By comparison arguments and iteration technique, the global stability of the semi-trivial boundary equilibrium and the positive equilibrium are addressed, respectively.

Key words: predator-prey model, stage structure, time delay, stability, Hopf bifurcation

CLC Number: