Predator-prey dynamics with square root functional responses

Nonlinear Analysis: Real World Applications

Volumn 13, Issue 4, 2012, Pages 1837-1843

  Braza, Peter A ^a  

^a UNIVERSITY OF NORTH FLORIDA   (United States)

Author keywords

Hopf bifurcation; Modified LotkaVolterra; Predatorprey; Square root response function

Indexed keywords

FUNCTIONAL RESPONSE; INTERACTION TERM; LOTKA-VOLTERRA; PREDATOR-PREY; PREDATOR-PREY DYNAMICS; PREDATOR-PREY MODELS; SOLUTION BEHAVIOR; SQUARE ROOTS; STANDARD MODEL;

NONLINEAR ANALYSIS; NONLINEAR SYSTEMS;

HOPF BIFURCATION;

EID: 84856549585     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.12.014     Document Type: Article

References (25)

1. V. Ajraldi, M. Pittavino, and E. Venturino Modeling Herd behavior in population systems Nonlinear Anal. RWA 12 2011 2319 2338
2. Y. Kuang, and E. Beretta Global qualitative analysis of a ratio-dependent predatorprey system J. Math. Biol. 36 1998 389 406 (Pubitemid 128735354)
3. S.-B. Hsu, T.-W. Hwang, and Y. Kuang A ratio-dependent food chain model and its applications to biological control Math. Biosciences 181 2003 55 83 (Pubitemid 35379445)
4. B. Li, and Y. Kuang Heteroclinic bifurcation in the MichaelisMenten-type ratio-dependent predatorprey system SIAM J. Appl. Math. 67 5 2007 1453 1464 (Pubitemid 47613215)
5. P.H. Leslie Some further notes on the use of matrices in population mathematics Biometrica 35 1948 213 245
6. J.T. Tanner The stability and intrinsic growth rates of prey and predator populations Ecology 56 1975 855 867
7. R.M. May Stability and Complexity in Model Ecosystems 1973 Princeton University Press Princeton, NJ
8. E. Saez, and E. Gonzales-Olivares Dynamics of a predatorprey model SIAM J. Appl. Math. 59 1999 1867 1878
9. P.A. Braza Predatorprey dynamics with disease in the prey Math. Biosciences 2 4 2005 703 717
10. C. Cosner, and D.L. DeAngelis Effects of spatial grouping on the functional response of predators Theoretical, Population Biology 56 1999 65 75 (Pubitemid 29395865)
11. J. Chattopadhyay, S. Chatterjee, and E. Venturino Patchy agglomeration as a transition from monospecies to recurrent plankton blooms J. Theoretical Biology 253 2008 289 295
12. G. Zeng, F. Wang, and J.J. Nieto Complexity of a delayed predatorprey model with impulsive Harvest and Holling type II functional response Adv. Complex Syst. 11 2008 77 97
13. L. Wang, L. Chen, and J.J. Nieto The dynamics of an epidemic model for pest control with impulsive effect Nonlinear Anal. RWA 11 2010 1374 1386
14. J. Hou, Z. Teng, and S. Gao Permanence and global stability for nonautonomou N-species LotkaVolterra competitive system with impulses Nonlinear Anal. RWA 11 2010 1882 1896
15. R.M. May Time delay versus stability in population models with two and three trophic levels Ecology 4 1973 315 325
16. H. Hu, and L. Huang Stability and Hopf Bifurcation in a delayed predatorprey system with stage structure for prey Nonlinear Anal. RWA 11 2010 2757 2769
17. W. Zuo, and J. Wei Stability and Hopf bifurcation in a diffusive predatorprey system with delay effect Nonlinear Anal. RWA 12 2011 1998 2011
18. M. Haque A detailed study of the BeddingtonDeAngelis predatorprey model Math. Biosci. 234 2011 1 16
19. G. Buffoni, M. Groppi, and C. Soresina Effects of prey over-undercrowding in predatorprey systems with prey-dependent trophic functions Nonlinear Anal. RWA 12 2011 2871 2887
20. C.S. Holling The functional response of invertebrate predator to prey density Mem. Ent. Soc. Can. 45 1965 3 60
21. P.A. Braza The bifurcation structure of the HollingTanner model for predatorprey interactions using two-timing SIAM J. Appl. Math. 63 3 2003 889 904
22. Francesco M. Scudo, and James R. Ziegler The golden age of theoretical ecology: 19231940 A Collections of Works by V. Volterra, V.S. Kostitzin, A.J. Lotka and A.N. Kolmogoroff 1971 Spring-Verlag New York
23. J. Carr Applications of Centre Manifold Theory 1981 Springer-Verlag New York
24. E.J. Doedel, J.P. Kernevez, AUTO, Software continuations and bifurcation problems in ordinary differential equations, Technical Report, California Institute of Technology, Pasadena, CA, 1986.
25. Bard Ermentrout Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students 2002 SIAM Press Philadelphia, PA