The hopf bifurcation for a predator-prey system with θ -logistic growth and prey refuge

Abstract and Applied Analysis

Volumn 2013, Issue , 2013, Pages

  Wang, Shaoli ^a   Ge, Zhihao ^a  

^a HENAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84881492705     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/168340     Document Type: Article

References (19)

1. Holling C. S., Some characteristics of simple types of predation and parasitism. Canadian Entomologist 1959 91 385 398
2. Hassell M. P., May R. M., Stability in insect host-parasite models. Journal of Animal Ecology 1973 42 693 726
3. Smith J. M., Models in Ecology 1974 Cambridge, UK Cambridge University
4. Hassell M. P., The Dynamics of Arthropod Predator-Prey Systems 1978 13 Princeton, NJ, USA Princeton University MR508052 ZBL0429.92018
5. Ji L., Wu C., Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge. Nonlinear Analysis: Real World Applications 2010 11 4 2285 2295 10.1016/j.nonrwa.2009.07. 003 MR2661899 ZBL1203.34070
6. Sih A., Prey refuges and predator-prey stability. Theoretical Population Biology 1987 31 1 1 12 10.1016/0040-5809(87)90019-0 MR878314
7. Taylor R. J., Predation 1984 New York, NY, USA Chapman and Hall
8. González-Olivares E., Ramos-Jiliberto R., Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability. Ecological Modelling 2003 166 135 146 (Pubitemid 37537755)
9. Krivan V., Effects of optimal antipredator behavior of prey on predator-prey dynamics: the role of refuges. Theoretical Population Biology 1998 53 131 142 (Pubitemid 28417976)
10. Ma Z., Li W., Zhao Y., Wang W., Zhang H., Li Z., Effects of prey refuges on a predator-prey model with a class of functional responses: the role of refuges. Mathematical Biosciences 2009 218 2 73 79 10.1016/j.mbs.2008.12.008 MR2513672 ZBL1160.92043
11. Chen L., Chen F., Chen L., Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge. Nonlinear Analysis: Real World Applications 2010 11 1 246 252 10.1016/j.nonrwa.2008.10.056 MR2570544 ZBL1186.34062
12. Tao Y. D., Wang X., Song X. Y., Effect of prey refuge on a harvested predator prey model with generalized functional response. Communications in Nonlinear Science and Numerical Simulation 2010 16 1052 1059
13. Ko W., Ryu K., A qualitative study on general Gause-type predator-prey models with constant diffusion rates. Journal of Mathematical Analysis and Applications 2008 344 1 217 230 10.1016/j.jmaa.2008.03.006 MR2416302 ZBL1144.35029
14. Tsoularis A., Wallace J., Analysis of logistic growth models. Mathematical Biosciences 2002 179 1 21 55 10.1016/S0025-5564(02)00096-2 MR1908735 ZBL0993.92028 (Pubitemid 34686426)
15. Hale J., Theory of Functional Differential Equations 1977 Heidelberg, Germany Springer MR0508721
16. Beretta E., Kuang Y., Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM Journal on Mathematical Analysis 2002 33 5 1144 1165 10.1137/S0036141000376086 MR1897706 ZBL1013.92034
17. Hassard B. D., Kazarinoff N. D., Wan Y. H., Theory and Applications of Hopf Bifurcation 1981 41 Cambridge, UK Cambridge University Press MR603442
18. Ge Z., Yan J., Hopf bifurcation of a predator-prey system with stage structure and harvesting. Nonlinear Analysis: Theory, Methods & Applications 2011 74 2 652 660 10.1016/j.na.2010.09.019 MR2733238 ZBL1207.34106
19. Xu R., Gan Q., Ma Z., Stability and bifurcation analysis on a ratio-dependent predator-prey model with time delay. Journal of Computational and Applied Mathematics 2009 230 1 187 203 10.1016/j.cam.2008.11.009 MR2532302 ZBL1186.34123