Stability and bifurcation analysis for a delayed Lotka-Volterra predator-prey system

Journal of Computational and Applied Mathematics

Volumn 196, Issue 1, 2006, Pages 198-210

  Yan, Xiang Ping ^a   Chu, Yan Dong ^a  

^a LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

Hopf bifurcation; Periodic solutions; Predator prey system; Stability; Time delay

Indexed keywords

BIFURCATION (MATHEMATICS); LINEAR EQUATIONS; NUMERICAL ANALYSIS; SYSTEM STABILITY; SYSTEMS ANALYSIS;

HOPF BIFURCATION; LOTKA-VOLTERRA PREDATOR-PREY SYSTEM; PERIODIC SOLUTIONS; TIME DELAY;

TIME VARYING SYSTEMS;

EID: 33745678050     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.09.001     Document Type: Article

References (16)

1. Beretta E., and Kuang Y. Convergence results in a well-known delayed predator-prey system. J. Math. Anal. Appl. 204 (1996) 840-853
2. Chow S.-N., and Hale J.K. Methods of Bifurcation Theory (1982), Springer, New York
3. Faria T. Stability and bifurcation for a delayed predator-prey model and the effect of diffusion. J. Math. Anal. Appl. 254 (2001) 433-463
4. Faria T., and Magalhães L.T. Normal form for retarded functional differential equations and applications to Bogdanov-Takens singularity. J. Differential Equations 122 (1995) 201-224
5. Freedman H.I., and Rao V.S.H. Stability for a system involving two time delays. SIAM. J. Appl. Math. 46 (1986) 552-560
6. Freedman H.I., and Ruan S. Uniform persistence in functional differential equations. J. Differential Equations 115 (1995) 173-192
7. Hale J.K. Theory of Functional Differential Equations (1977), Springer, New York
8. Hale J.K., Infante E.F., and Tsen F.-S.P. Stability in linear delay equations. J. Math. Anal. Appl. 105 (1985) 533-555
9. He X. Stability and delays in a predator-prey system. J. Math. Anal. Appl. 198 (1996) 355-370
10. Kuang Y. Delay Differential Equations with Application in Population Dynamics (1993), Academic Press, New York
11. Liu Z., and Yuan R. Stability and bifurcation in a harmonic oscillator with delays. Choas, Solitons Fractals 23 (2005) 551-562
12. Ma W., and Takeuchi Y. Stability analysis on a predator-prey system with distributed delays. J. Comput. Appl. Math. 88 (1998) 79-94
13. Wang W., and Ma Z. Harmless delays for uniform persistence. J. Math. Anal. Appl. 158 (1991) 256-268
14. Wei J., and Li M. Global existence of periodic solutions in a tri-neuron network model with delays. Physica D 198 (2004) 106-119
15. Wei J., and Ruan S. Stability and bifurcation in a neural network model with two delays. Physica D 130 (1999) 255-272
16. Zhao T., Kuang Y., and Smith H.L. Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems. Nonlinear Anal. 28 (1997) 1373-1394