Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure

Nonlinear Dynamics

Volumn 49, Issue 1-2, 2007, Pages 285-294

  Qu, Ying ^a   Wei, Junjie ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Hopf bifurcation; Periodic solution; Prey predator; Time delay

Indexed keywords

COMPUTER SIMULATION; HOPF BIFURCATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PROBLEM SOLVING; TIME VARYING SYSTEMS;

PERIODIC SOLUTIONS; PREY-PREDATOR; TIME-DELAY MODELS;

TIME DELAY;

EID: 34248370155     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-9133-x     Document Type: Article

References (11)

1. Adimy, M., Crauste, F., Ruan, S.: Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull. Math. Biol. DOT: 10.1007/s11538-006-9121-9 (2006)
2. Aiello, W.G., Freedman, H.I.: A time-delay model of single-species growth with stage structure. Math. Biosci. 101, 139-153 (1990)
3. Aiello, W.G., Freedman, H.I., Wu, J.: Analysis of a model representing stage-structured population growth with state-dependant time delay. SIAM J. Appl. Math. 52, 855-869 (1992)
4. Beretta, E., Kuang, Y.: Geometric stability switch criteria in delay differential systems with delay dependant parameters. SIAM. J. Math. Anal. 33, 1144-1165 (2002)
5. Cooke, K., van den Driessche, P., Zou, X.: Interaction of maturation delay and nonlinear birth in population and epidemic models. J. Math. Biol. 39, 332-352 (1999)
6. Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)
7. Hassard, B., Kazarinoff, N., Wan, Y.: Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge (1981)
8. Liu, S., Chen, L., Luo, G., Jiang, Y.: Asymptotic behaviors of competitive Lotka-Volterra system with stage structure. J. Math. Anal. Appl. 271, 124-138 (2002)
9. Song, X., Chen, L.: Optimal harvesting and stability for a two species competitive system with stage structure. Math. Biosci. 170, 173-186 (2001)
10. Satio, Y., Takeuchi, Y.: A time-delay model for prey-predator growth with stage structcure. Canad. Appl. Math. Quat., in press (2006)
11. Wei, J., Li, M.Y.: Hopf bifurcation analysis in a delayed Nicholson blowflies equation. Nonlinear Anal. 60, 1351-1367 (2005)