Consequences of Allee Effects on Stability Analysis of the Population Model Xt+1=lXtf(Xt-3)

References (17)

1. Allee, W. C. Animal Aggretions: A Study in General Sociology (University of Chicago Press, Chicago, 1931).
2. Allen, L. J. S. An Introduction to Mathematical Biology (Pearson, New Jersey, 2007).
3. Courchamp, F., Berec L. and Gascoigne, J. Allee Effects in Ecology and Conservation (Oxford University Press, New York, 2008). C¸ elik, C., Merdan, H., Duman O. and Akın, ¨O. Allee effects on population dynamics with delay, Chaos, Solitons & Fractals 37, 65–74, 2008.
4. Cunningham, K., Kulenovi´c, M. R. S., Ladas, G. and Valicenti, S. V. On the recursive se- quences xn+1= (α + βxn)/(Bxn+ Cxn−1), Nonlinear Anal. 47, 4603–4614, 2001.
5. Duman, O. and Merdan, H. Stability analysis of continuous population model involving predation and Allee effect, Chaos, Solitons & Fractals 41, 1218–1222, 2009.
6. Elaydi, S. N. An Introduction to Difference Equations (Springer, New York, 2006).
7. Fowler, M. S. and Ruxton, G. D. Population dynamic consequences of Allee effects, J Theor Biol 215, 39–46, 2002.
8. Hale, J. and Ko¸cak, H. Dynamics and Bifurcation (Springer-Verlag, New York, 1991).
9. Jang, S. R. J. Discrete-time host-parasitoid models with Allee effects: Density dependence versus parasitism, J. Diffence Equ. Appl 17, 525–539, 2011. Kulenovi´c, M. R. S., Ladas, G. and Prokup, N. R. A rational difference equations, Comput Math Appl. 41, 671-678, 2001. L´opez-Ruiz, R. and Fournier-Prunaret, D. Indirect Allee effect, bistability and chaotic os- cillations in a predator-prey discrete model of logistic type, Chaos, Solitons & Fractals 24, –101, 2005.
10. McCarthy, M. A. The Allee effect, finding mates and theoretical models, Ecological Mod- elling 103, 99–102, 1997.
11. Merdan, H. and Duman, O. On the stability analysis of a general discrete-time population model involving predation and Allee effects, Chaos, Solitons & Fractals 40, 1169–1175, 2009.
12. Merdan, H., Duman, O., Akın, ¨O and C¸ elik, C. Allee effects on population dynamics in continous (overlaping) case, Chaos, Solitons & Fractals 39, 1994–2001, 2009.
13. Merdan, H. and Ak G¨um¨u¸s, O. A. Stability analysis of a general discrete-time population model involving delay with Allee effects, Appl. Math. and Comp. 219, 1821–1832, 2012.
14. Merdan, H. Stability analysis of a Lotka-Volterra type predator-prey system involving Allee effects, ANZIAM J. 52, 139–145, 2010.
15. Murray, J. D. Mathematical Biology (Springer-Verlag, New York, 1993).
16. Scheuring, I. Allee effect increases the dynamical stability of populations, J Theor. Biol., 407–414, 1999.
17. Sophia, R. and Jan