Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$

KARAOĞLU, E.; MERDAN, H.

Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$

H. MERDAN, (TOBB Ekonomi ve Teknoloji Üniversitesi, Matematik Bölümü, Ankara, Türkiye)

E. KARAOĞLU (TOBB Ekonomi ve Teknoloji Üniversitesi, Matematik Bölümü, Ankara, Türkiye)

Hacettepe Journal of Mathematics and Statistics

4 0

Yıl: 2012 Cilt: 41 Sayı: 5 Sayfa Aralığı: 51 - 765 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$

Öz:

The stability conditions of equilibrium points of the popul ation model $X_{t+1}=lambda X_tf(X_{t-3})$ with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population de nsity. Analysis and numerical simulations show that Allee effects h ave both stabilizing and destabilizing effects on population dynamics with delay.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[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).
[4] Celik, C., Merdan, H., Duman O. and Akın, O.Allee effects on population dynamics with delay, Chaos, Solitons & Fractals 37, 65–74, 2008.
[5] Cunningham, K., Kulenovic, M.R. S., Ladas, G. and Valic enti, S.V. On the recursive se-quences x n+1= (α+βx n)/(Bx n+Cxn−1), Nonlinear Anal.47, 4603–4614, 2001.
[6] Duman, O. and Merdan, H. Stability analysis of continuous population model involving predation and Allee effect, Chaos, Solitons & Fractals 41, 1218–1222, 2009.
[7] Elaydi, S.N. An Introduction to Difference Equations (Springer, New York, 2006).
[8] Fowler, M.S. and Ruxton, G. D. Population dynamic consequences of Allee effects, J Theor Biol 215, 39–46, 2002.
[9] Hale, J. and Ko ̧cak, H. Dynamics and Bifurcation (Springer-Verlag, New York, 1991).
[10] Jang, S.R. J. Discrete-time host-parasitoid models with Allee effects: D ensity dependence versus parasitism, J. Diffence Equ. Appl 17, 525–539, 2011.
[11] Kulenovic, M.R.S., Ladas, G. and Prokup, N.R. A rational difference equations, Comput Math Appl. 41, 671-678, 2001.
[12] Lopez-Ruiz, R. and Fournier-Prunaret, D. Indirect Allee effect, bistability and chaotic os- cillations in a predator-prey discrete model of logistic ty pe, Chaos, Solitons & Fractals 24, 85–101, 2005.
[13] McCarthy, M.A. The Allee effect, finding mates and theoretical models, Ecological Mod- elling 103, 99–102, 1997.
[14] Merdan, H. and Duman, O. On the stability analysis of a general discrete-time popula tion model involving predation and Allee effects, Chaos, Solitons & Fractals 40, 1169–1175, 2009.
[15] Merdan, H., Duman, O., Akın, O and Celik, C. Allee effects on population dynamics in continous (overlaping) case, Chaos, Solitons & Fractals 39, 1994–2001, 2009.
[16] 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.
[17] Merdan, H. Stability analysis of a Lotka-Volterra type predator-prey system involving Allee effects, ANZIAM J. 52, 139–145, 2010.
[18] Murray, J. D. Mathematical Biology (Springer-Verlag, New York, 1993).
[19] Scheuring, I.Allee effect increases the dynamical stability of populatio ns, J Theor. Biol. 199, 407–414, 1999.
[20] Sophia, R. and Jang, J. Allee effects in a discrete-time host-parasitoid model with stage structure in the host, Disc. & Cont. Dyn. Sys. -B 8, 145–159, 2007
[21] Stephens, P.A. and Sutherland, W.J. Consequences of the Allee effect for behaviour, ecology and conservation, Trends in Ecology & Evolution 14, 401–405, 1999
[22] Zhou, S.R, Liu, Y.F and Wang, G. The stability of predator-prey systems subject to the Allee effects, Theor. Population Biol. 67, 23–31, 2005.

APA	MERDAN H, KARAOĞLU E (2012). Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. , 51 - 765.
Chicago	MERDAN H.,KARAOĞLU E. Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. (2012): 51 - 765.
MLA	MERDAN H.,KARAOĞLU E. Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. , 2012, ss.51 - 765.
AMA	MERDAN H,KARAOĞLU E Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. . 2012; 51 - 765.
Vancouver	MERDAN H,KARAOĞLU E Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. . 2012; 51 - 765.
IEEE	MERDAN H,KARAOĞLU E "Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$." , ss.51 - 765, 2012.
ISNAD	MERDAN, H. - KARAOĞLU, E.. "Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$". (2012), 51-765.

APA	MERDAN H, KARAOĞLU E (2012). Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. Hacettepe Journal of Mathematics and Statistics, 41(5), 51 - 765.
Chicago	MERDAN H.,KARAOĞLU E. Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. Hacettepe Journal of Mathematics and Statistics 41, no.5 (2012): 51 - 765.
MLA	MERDAN H.,KARAOĞLU E. Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. Hacettepe Journal of Mathematics and Statistics, vol.41, no.5, 2012, ss.51 - 765.
AMA	MERDAN H,KARAOĞLU E Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. Hacettepe Journal of Mathematics and Statistics. 2012; 41(5): 51 - 765.
Vancouver	MERDAN H,KARAOĞLU E Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$. Hacettepe Journal of Mathematics and Statistics. 2012; 41(5): 51 - 765.
IEEE	MERDAN H,KARAOĞLU E "Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$." Hacettepe Journal of Mathematics and Statistics, 41, ss.51 - 765, 2012.
ISNAD	MERDAN, H. - KARAOĞLU, E.. "Consequences of Allee effects on stability analysis of the population model $X_{t+1}=lambda X_tf(X_{t-3})$". Hacettepe Journal of Mathematics and Statistics 41/5 (2012), 51-765.