Stability and Hopf bifurcation for a delayed prey-predator system with diffusion effects

Applied Mathematics and Computation

Volumn 192, Issue 2, 2007, Pages 552-566

  Yan, Xiang Ping ^a  

^a LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

Diffusion; Hopf bifurcation; Periodic solution; Prey predator system; Stability; Time delay

Indexed keywords

COMPUTER SIMULATION; FUNCTIONAL ANALYSIS; LINEAR SYSTEMS; NUMERICAL METHODS; TIME DELAY;

PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS; POSITIVE EQUILIBRIUM; PREY-PREDATOR SYSTEM;

HOPF BIFURCATION;

EID: 34548849467     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.03.033     Document Type: Article

References (13)

1. Busenberg S., and Huang W. Stability and Hopf bifurcation for a population delay model with diffusion effects. J. Diff. Eqs. 124 (1996) 80-127
2. Faria T. Stability and bifurcation for a delayed predator-prey model and the effect of diffusion. J. Math. Anal. Appl. 254 (2001) 433-463
3. Faria T. Normal forms and Hopf bifurcation for partial differential equations with delays. Trans. Amer. Math. Soc. 352 (2000) 2217-2238
4. Green D., and Stech H. Diffusion and hereditary effects in a class of population models. In: Busenberg S., and Cooke C. (Eds). Differential Equations and Applications in Ecology, Epidemics and Population Problems (1981), Academic Press 19-28
5. Hale J.K. Theory of Functional Differential Equations (1977), Spring-Verlag, New York
6. He X. Stability and delays in a predator-prey system. J. Math. Anal. Appl. 198 (1996) 355-370
7. Kuang Y., and Smith H.L. Global stability in diffusive delay Lotka-Volterra systems. Diff. Integral Eqs. 4 (1991) 117-128
8. Kuang Y., and Smith H.L. Convergence in Lotka-Volterra type diffusive delay systems without dominating instantaneous negative feedbacks. J. Austral. Math. Soc. Ser. B (1991)
9. Wang W., and Ma Z. Harmless delays for uniform persistence. J. Math. Anal. Appl 158 (1991) 256C-268C
10. Murray J.D. Mathematical biology. 2nd ed. (1998), Springer-Verlag, Berlin
11. Wu J. Theory and Applications of Partial Functional Differential Equations (1996), Springer-Verlag, New York
12. Yoshida K. The Hopf bifurcation and its stability for semilinear diffusion equations with time delay arising in ecology. Hiroshima Math. J. 12 (1982) 321-348
13. Zhou L., Tang Y., and Hussein S. Stability and Hopf bifurcation for a delay competition diffusion system. Chaos, Solitons and Fractals 14 (2002) 1201-1225