Existence of positive periodic solutions for an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays

Applied Mathematics and Computation

Volumn 215, Issue 9, 2010, Pages 3390-3398

  Luo, Zhenguo ^a   Dai, Binxiang ^a   Zhang, Qianhong ^a,b  

^a CENTRAL SOUTH UNIVERSITY   (China)

^b HUNAN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Coincidence degree; Delay; Dispersion; Periodic solution; Pulse; Semi ratio dependent predator prey model

Indexed keywords

COINCIDENCE DEGREE; CONTINUATION THEOREM OF COINCIDENCE DEGREE THEORY; EXISTENCE OF POSITIVE PERIODIC SOLUTIONS; PERIODIC SOLUTION; POSITIVE PERIODIC SOLUTION; RATIO-DEPENDENT PREDATOR-PREY MODEL; SUFFICIENT CONDITIONS;

TIME DELAY;

DISPERSIONS;

EID: 71649112786     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.10.032     Document Type: Article

References (17)

1. Bai{dotless}̌nov D.D., and Simeonov P.S. Systems with Impulse Effect: Stability, Theory and Applications (1989), John Wiley & Sons, Inc., New York
2. Bai{dotless}̌nov D., and Simeonov P. Impulsive Differential Equations: Periodic Solutions and Applications (1993), John Wiley & Sons, Inc., New York
3. Bohner M., Fan M., and Zhang J. Existence of periodic solutions in predator-prey and competition dynamic systems. Nonlinear Anal. Real World Appl. 7 (2006) 1193-1204
4. Dai B., Su H., and Hu D. Periodic solution of a delayed ratio-dependent predator-prey model with monotonic functional response and impulse. Nonlinear Anal. 70 (2009) 126-134
5. Ding X. Periodicity in a delayed semi-ratio-dependent predator-prey system. Appl. Math. J. Chin. Univ. Ser. B 20 (2005) 151-158
6. Ding X., and Wang F. Positive periodic solution for a semi-ratio-dependent predator-prey system with diffusion and time delays. Nonlinear Anal. Real World Appl. 9 (2008) 239-249
7. Gaines R.E., and Mawkin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag, Berlin
8. Huo H.-F. Periodic solutions for a semi-ratio-dependent predator-prey system with functional responses. Appl. Math. Lett. 18 (2005) 313-320
9. Lakshmikantham V., Bai{dotless}̌nov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific Publishing Co., Inc., Teaneck, NJ
10. Liu B., Teng Z., and Liu W. Dynamic behaviors of the periodic Lotka-Voterra competing system with impulsive perturbations. Chaos Solitons Fractals 31 (2007) 356-370
11. Shen J., and Li J. Existence and global attractivity of positive periodic solutions for impulsive predator-prey model with dispersion and time delays. Nonlinear Anal. Real World Appl. 10 (2009) 227-243
12. Song X., and Chen L. Persistence and global stability for nonautonomous predator-prey system with diffusion and time delay. Comput. Math. Appl. 35 (1998) 33-40
13. Wang Q., Dai B., and Chen Y. Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response. Math. Comput. Model. 49 (2009) 1829-1836
14. Wang Q., Fan M., and Wang K. Dynamics of a class of nonautonomous semi-ratio-dependent predator-prey systems with functional responses. J. Math. Anal. Appl. 278 (2003) 443-471
15. Xu R., Chaplain M.A.J., and Davidson F.A. Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. Appl. Math. Comput. 148 (2004) 537-560
16. Zhang J., Chen L., and Chen X.D. Persistence and global stability for two-species nonautonomous competition Lotka-Volterra patch-system with time delay. Nonlinear Anal. Ser. A: Theory Methods 37 (1999) 1019-1028
17. Zhang S., Dong L., and Chen L. The study of predator-prey system with defensive ability of prey and impulsive perturbations on the predator. Chaos Solitons Fractals 23 (2005) 631-643