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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 29, Issue 1, Pages 35 - 52 (April 2008)


COMPLEX DYNAMICS IN A DELAY PREDATOR-PREY MODEL WITH SELECTIVE RECRUITMENT AND MIXED FUNCTIONAL RESPONSE

Rongping Zhu (P. R. China) and Hong Zhang (P. R. China)

Received September 4, 2007; Revised February 23, 2008

References:



[1] M. A. Aziz-Alaoui, Study of a Leslie-Gower-type tritrophic population model, Chaos Solitons Fractals 14 (2002), 1275-1293.

[2] M. A. Aziz-Alaoui and M. Daher Okiye, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Appl. Math. Lett. 16 (2003), 1069-1075.

[3] J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol. 44 (1975), 331-340.

[4] R. Bellman and K. Cooke, Differential Difference Equations, Academic Press, 1963.

[5] D. L. DeAngelis, R. A. Goldstein and R. V. O’Neill, A model for trophic interaction, Ecology 56 (1975), 881-892.

[6] J. K. Hale, Theory of Functional Differential Equations, Springer, New York, 1977.

[7] B. D. Hassard, N. D. Kazarionoff and Y. N. Wan, Theory and Application of Hopf Bifurcation, Cambridge University, Cambridge, 1981.

[8] Yang Kuang, Delay Differential Equations with Applications in Population Dynamics, Springer, New York, 1993.

[9] X. Song and L. Chen, Optimal harvesting and stability for a two species competitive system with stage structure, Math. Biosci. 170 (2001), 173-186.

Keywords and phrases: predator-prey model, equilibrium, Hopf bifurcation, uniform persistence, global stability.

 


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