Research Article
The Local Stability Analysis of a Nonlinear Discrete-Time Population Model with Delay and Allee Effect
Abstract
In
this work, we present a delay general nonlinear discrete-time population model
with and without Allee effects which occur at low population density. We
investigated local stability conditions of equilibrium point of both models and
we compared the local stability of the same equilibrium point of these two
models. Obtained all theoretical results were supported by numerical
simulations.
References
- [1]. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, New York, Academic Press, 1993.
- [2]. Allen and J. S. Linda, An Introduction to Mathematical Biology, Texas Tech. University, 2007.
- [3]. J. D. Murray, Mathematical Biology, New York , 2002.
- [4]. C. Çelik, H. Merdan, O. Duman , Ö. Akın, Allee effects on popülation dynamics with delay, Chaos, Solitons & Fractals Chaos, 39 (2009), 1994-2001.
- [5]. H. Merdan, O. Duman, Ö. Akın, C. Çelik, Allee effects on population dynamics in countinuous (overlapping)case, Chaos, Solitons & Fractals Chaos, 37 (2008), 65-74.
- [6]. H. Merdan, O. Duman, On the stability analysis of a general discrete-time population model involving predation and Allee effects, Chaos, Solitons & Fractals Chaos, 40 (2009), 1169-1175.
- [7]. H. Merdan, O. Ak Gumus, Stability analysis of a general discrete-time population model involving delay and Allee effects, Applied Mathematics and Computation, 219 (2012) 1821-1832.
- [8]. O. Ak. Gumus, H. Kose, On the stability of delay population dynamics related with Allee effects, Mathematical and Computational Applications, 17 (2012) 56-67 . [9]. W.C. Allee, Animal Agretions: A Study in General Sociology, University of Chicago Press, Chicago,1931.
- [10]. F. Brauer, C. Castillo-Chavez, Mathematical models in population biology and epidemiology, 2012 . [11]. O. Ak Gümüş, F. Kangalgil, Allee effect and stability in discrete-time host-parasitoid model, Journal of Advanced Research in Applied Mathematics, 7 (2015), 94-99.
- [12]. O. Ak Gumus, Local stability and the Allee effect in nonlinear discrete-time population models with delay, Journal of Advanced Research in Applied Mathematics, 7 (3) (2015) 30-37.
- [13]. F. Kangalgil, O. Ak. Gümüş, Allee effect in a new population model and stability analysis, General Mathematics Notes, 35 (1) (2016) 54-64.
Gecikmeli ve Allee Etkili Lineer Olmayan Ayrık-Zamanlı bir Popülasyon Modelinin Lokal Kararlılık Analizi
Abstract
Bu çalışmada, genel lineer olmayan ayrık zamanlı gecikmeli bir
popülasyon modeli, düşük popülasyon yoğunluğunda ortaya çıkan Allee etkisiyle
ve Allee etkisiz olarak ele alınmıştır.
Her iki modelin, denge noktasında lokal kararlılık şartları incelendik
ve bu iki modelin lokal kararlılıklarını karşılaştırdık. Elde edilen tüm teorik
sonuçlar nümerik simülasyonlar ile desteklenmiştir.
References
- [1]. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, New York, Academic Press, 1993.
- [2]. Allen and J. S. Linda, An Introduction to Mathematical Biology, Texas Tech. University, 2007.
- [3]. J. D. Murray, Mathematical Biology, New York , 2002.
- [4]. C. Çelik, H. Merdan, O. Duman , Ö. Akın, Allee effects on popülation dynamics with delay, Chaos, Solitons & Fractals Chaos, 39 (2009), 1994-2001.
- [5]. H. Merdan, O. Duman, Ö. Akın, C. Çelik, Allee effects on population dynamics in countinuous (overlapping)case, Chaos, Solitons & Fractals Chaos, 37 (2008), 65-74.
- [6]. H. Merdan, O. Duman, On the stability analysis of a general discrete-time population model involving predation and Allee effects, Chaos, Solitons & Fractals Chaos, 40 (2009), 1169-1175.
- [7]. H. Merdan, O. Ak Gumus, Stability analysis of a general discrete-time population model involving delay and Allee effects, Applied Mathematics and Computation, 219 (2012) 1821-1832.
- [8]. O. Ak. Gumus, H. Kose, On the stability of delay population dynamics related with Allee effects, Mathematical and Computational Applications, 17 (2012) 56-67 . [9]. W.C. Allee, Animal Agretions: A Study in General Sociology, University of Chicago Press, Chicago,1931.
- [10]. F. Brauer, C. Castillo-Chavez, Mathematical models in population biology and epidemiology, 2012 . [11]. O. Ak Gümüş, F. Kangalgil, Allee effect and stability in discrete-time host-parasitoid model, Journal of Advanced Research in Applied Mathematics, 7 (2015), 94-99.
- [12]. O. Ak Gumus, Local stability and the Allee effect in nonlinear discrete-time population models with delay, Journal of Advanced Research in Applied Mathematics, 7 (3) (2015) 30-37.
- [13]. F. Kangalgil, O. Ak. Gümüş, Allee effect in a new population model and stability analysis, General Mathematics Notes, 35 (1) (2016) 54-64.
There are 11 citations in total.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | September 30, 2017 |
| Submission Date | March 1, 2017 |
| Acceptance Date | May 30, 2017 |
| Published in Issue | Year 2017 |