Allee effects in a discrete-time host-parasitoid model with stage structure in the host

Discrete and Continuous Dynamical Systems - Series B

Volumn 8, Issue 1, 2007, Pages 145-159

  Jang, Sophia R J ^a  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

Author keywords

Allee effects; Extinction; Population threshold

Indexed keywords

EID: 34548679857     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.8.145     Document Type: Conference Paper

References (16)

1. W.C. Allee, "The Social Life of Animals," William Heinemann, 1938.
2. L. J.-S. Allen, "An Introduction to Mathematical Biology," Prentice-Hall, 2006.
3. M. Begon, J. Harper and C. Townsend, "Ecology: Individuals, Populations and Communities," Blackwell Science Ltd, New York, 1996.
4. J.M. Cushing, The Allee effect in age-structured population dynamics, in "Mathematical Ecology"(ed. T. Hallam, L. Gross and S. Levin), (1988), 479-505.
5. B. Dennis, Allee effects, population growth, critical density, and the chance of extinction, Nat. Res. Mod., 3 (1989), 481-538.
6. B. Dennis, Allee effects in stochastic populations, Oikos, 96 (2002), 389-401.
7. A. Grove and G. Ladas, "Periodicities in Nonlinear Difference Equations," CRC Press, 2005.
8. S. R.-J. Jang and A.S. Ackleh, Discrete-time, discrete stage-structured predator-prey models, J. Diff. Equ. Appl., 11 (2005), 399-413.
9. S. R.-J. Jang, Allee effects in a host-parasitoid model, J. Diff. Equ. Appl., 12 (2006), 165-182.
10. S. R.-J. Jang and S. L. Diamond, A host-parasitoid interaction with Allee effects on the host, Compu. Math. Appl., in press.
11. M. Kulenovic and A. Yakubu, Compensatory versus overcompensatory dynamics in density-dependent Leslie models, J. Diff. Equ. Appl., 10 (2004), 1251-1265.
12. R.M. May, M. Hassell, R. Anderson and D. Tonkyn, Density dependence in host-parasitoid models, J. Ani. Ecol., 50 (1981), 855-865.
13. A. Morozov, S. Petrovskii and B.-L. Li, Bifurcations and chaos in a predator-prey system with the Allee effect, Proceedings of the Royal Society, Ser. B, 271 (2004), 1407-1414.
14. S. Schreiber, Allee effects, extinctions, and chaotic transients in simple population models, Theo. Pop. Biol., 64 (2003), 201-209.
15. A. Yakubu, Multiple attractors in juvenile-adult single species models, J. Diff. Eq. Appl., 9 (2003), 1083-1098.
16. S. Zhou, Y. Liu and G. Wang, The stability of predator-prey systems subject to the Allee effects, Theo. Pop. Biol., 67 (2005), 23-31.