Bifurcation analysis in a predatorprey system with stage-structure and harvesting

Journal of the Franklin Institute

Volumn 347, Issue 7, 2010, Pages 1097-1113

  Qu, Ying ^a   Wei, Junjie ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Harvesting; Hopf bifurcation; Predatorprey system; Stability; Time delay

Indexed keywords

ANALYTICAL RESULTS; BIFURCATION ANALYSIS; CENTER MANIFOLD THEOREM; NORMAL FORM THEORY; NUMERICAL SIMULATION; PERIODIC SOLUTION; POSITIVE STEADY STATE; PREDATOR - PREY SYSTEM; PREDATOR-PREY MODELS;

COMPUTER SIMULATION; HARVESTING; SYSTEM STABILITY; TIME DELAY;

HOPF BIFURCATION;

EID: 77955473046     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2010.03.017     Document Type: Article

References (16)

1. M. Adimy, F. Crauste, and S. Ruan Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases Bull. Math. Biol. 68 2006 2321 2351
2. W.G. Aiello, and H.I. Freedman A time-delay model of single-species growth with stage structure Math. Biosci. 101 1990 139 153
3. W.G. Aiello, H.I. Freedman, and J. Wu Analysis of a model representing stage-structured population growth with state-dependent time delay SIAM J. Appl. Math. 52 1992 855 869
4. E. Beretta, and Y. Kuang Geometric stability switch criteria in delay differential systems with delay-dependent parameters SIAM J. Math. Anal. 33 2002 1144 1165
5. F. Brauer, and A. Soudack Stability regions in predatorprey systems with constant rate prey harvesting J. Math. Biol. 8 1979 55 71
6. C. Clark Mathematical Bioeconomics: The Optimal Management of Renewable Resources second ed. 1990 Wiley New York
7. J.K. Hale, and M.V. Lunel Introduction to Functional Differential Equations 1993 Springer New York
8. B. Hassard, N. Kazarinoff, and Y. Wan Theory and Applications of Hopf Bifurcation 1981 Cambridge University Press Cambridge
9. T. Kar, and U. Pahari Modelling and analysis of a preypredator system with stage-structure and harvesting Nonlinear Anal. Real World Appl. 8 2007 601 609
10. S. Liu, L. Chen, G. Luo, and Y. Jiang Asymptotic behaviors of competitive LotkaVolterra system with stage structure J. Math. Anal. Appl. 271 2002 124 138
11. Y. Qu, and J. Wei Bifurcation analysis in a time-delay model for preypredator growth with stage-structure Nonlinear Dyn. 49 2007 285 294
12. S. Ruan On nonlinear dynamics of predatorprey models with discrete delay Math. Model. Nat. Phenom. 4 2009 140 187
13. X. Song, and L. Chen Optimal harvesting and stability for a two species competitive system with stage structure Math. Biosci. 170 2001 173 186 (Pubitemid 32303991)
14. Y. Saito, and Y. Takeuchi A time-delay model for preypredator growth with stage structure Can. Appl. Math. Q. 11 2003 293 302
15. J. Wei, and M.Y. Li Hopf bifurcation analysis in a delayed Nicholson blowflies equation Nonlinear Anal. 60 2005 1351 1367
16. J. Wei, and S. Ruan Stability and bifurcation in a neural network model with two delays Physica D 130 1999 255 272 (Pubitemid 129587672)