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Bifurcation Analysis of a Stage-Structured Prey-Predator System with Discrete and Continuous Delays

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DOI: 10.4236/am.2013.47144    2,828 Downloads   4,388 Views   Citations

ABSTRACT

A three-stage-structured prey-predator model with discrete and continuous time delays is studied. The characteristic equations and the stability of the boundary and positive equilibrium are analyzed. The conditions for the positive equilibrium occurring Hopf bifurcation are given, by applying the theorem of Hopf bifurcation. Finally, numerical simulation and brief conclusion are given.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. Li, W. Liu and X. Xue, "Bifurcation Analysis of a Stage-Structured Prey-Predator System with Discrete and Continuous Delays," Applied Mathematics, Vol. 4 No. 7, 2013, pp. 1059-1064. doi: 10.4236/am.2013.47144.

References

[1] W. Aiello and H. Freedman, “A Time-Delay Model of Single-Species Growth with Stage Structure,” Mathematical Biosciences, Vol. 101, No. 2, 1990, pp. 139-153. doi:10.1016/0025-5564(90)90019-U
[2] W. Wang and L. Chen, “A Predator-Prey System with Stage-Structure for Predator,” Computers & Mathematics with Applications, Vol. 33, No. 8, 1997, pp. 83-91. doi:10.1016/S0898-1221(97)00056-4
[3] S. Liu, L. Chen and R. Agarwal, “Recent Progress on Stage Structured Population Dynamics,” Mathematical and Computer Modelling, Vol. 36, No. 11-13, 2002, pp. 1319-1360. doi:10.1016/S0895-7177(02)00279-0
[4] S. Gao, “Global Stability of Three-Stage-Structured Single-Species Growth Model,” Journal Xinjiang University, Vol. 18, No. 12, 2001, pp. 154-158 (in Chinese).
[5] S. Yang and B. Shi. “Periodic Solution for a Three-Stage Structured Predator-Prey System with Time Delay,” Journal of Mathematical Analysis and Applications, Vol. 341, No. 1, 2008, pp. 287-294. doi:10.1016/j.jmaa.2007.10.025
[6] S. Li and X. Xue, “Hopf Bifurcation in a Three-Stage Structured Prey-Predator System with Predator Density Dependent,” Communications in Computer and Information Science, Vol. 288, 2012, pp. 740-747. doi:10.1007/978-3-642-31965-5_86
[7] S. Li, Y. Xue and W. Liu, “Hopf Bifurcation and Global Periodic Solutions for a Three-Stage-Structured Prey Predator System with Delays,” International Journal of Informationa and Systems Sciences, Vol. 8, No. 1, 2012, pp. 142-156.
[8] Z. Wang, “A Very Simple Criterion for Characterizing the Crossing Direction of Time-delayed Systems with Delay-Dependent Parameters,” International Journal of Bifurcation and Chaos, Vol. 22, No. 3, 2012, Article ID: 1250048. doi:10.1007/978-1-4612-9892-2
[9] J. Hale, “Theory of Functional Differential Equations,” Springer, New York, 1977.
[10] B. Hassard, N. Kazarinoff and Y. Wan, “Theory and Applications of Hopf Bifurcation,” Cambridge University Press, Cambridge, 1981.

  
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