Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes
Applications of Mathematics (2014)
- Volume: 59, Issue: 2, page 217-240
- ISSN: 0862-7940
Access Full Article
top
Abstract
topHow to cite
topTian, Yanling. "Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes." Applications of Mathematics 59.2 (2014): 217-240. <http://eudml.org/doc/261088>.
@article{Tian2014,
abstract = {A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant steady state is studied by analyzing the eigenvalues. Some simple and easily verifiable sufficient conditions for global stability are obtained by virtue of the stability of the related FDE and some monotonous iterative sequences. Numerical simulations and reasonable biological explanations are carried out to illustrate the main results and the justification of the model.},
author = {Tian, Yanling},
journal = {Applications of Mathematics},
keywords = {delayed diffusive predator-prey model; modified Leslie-Gower scheme; Holling-type II scheme; persistence; stability; eigenvalue; monotonous iterative sequence; delayed diffusive predator-prey model; modified Leslie-Gower scheme; Holling-type II scheme; persistence; stability; eigenvalue; monotonous iterative sequence},
language = {eng},
number = {2},
pages = {217-240},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes},
url = {http://eudml.org/doc/261088},
volume = {59},
year = {2014},
}
TY - JOUR
AU - Tian, Yanling
TI - Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 217
EP - 240
AB - A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant steady state is studied by analyzing the eigenvalues. Some simple and easily verifiable sufficient conditions for global stability are obtained by virtue of the stability of the related FDE and some monotonous iterative sequences. Numerical simulations and reasonable biological explanations are carried out to illustrate the main results and the justification of the model.
LA - eng
KW - delayed diffusive predator-prey model; modified Leslie-Gower scheme; Holling-type II scheme; persistence; stability; eigenvalue; monotonous iterative sequence; delayed diffusive predator-prey model; modified Leslie-Gower scheme; Holling-type II scheme; persistence; stability; eigenvalue; monotonous iterative sequence
UR - http://eudml.org/doc/261088
ER -
References
top- Aziz-Alaoui, M. A., Okiye, M. Daher, 10.1016/S0893-9659(03)90096-6, Appl. Math. Lett. 16 (2003), 1069-1075. (2003) MR2013074DOI10.1016/S0893-9659(03)90096-6
- Chen, B., Wang, M., 10.1016/j.camwa.2007.03.020, Comput. Math. Appl. 55 (2008), 339-355. (2008) Zbl1155.35390MR2384151DOI10.1016/j.camwa.2007.03.020
- Ko, W., Ryu, K., 10.1016/j.jde.2006.08.001, J. Differ. Equations 231 (2006), 534-550. (2006) MR2287896DOI10.1016/j.jde.2006.08.001
- Lindström, T., Global stability of a model for competing predators: An extension of the Ardito & Ricciardi Lyapunov function, Nonlinear Anal., Theory Methods Appl. 39 (2000), 793-805. (2000) Zbl0945.34037MR1733130
- Murray, J. D., Mathematical Biology, Vol. 1: An Introduction. 3rd ed, Interdisciplinary Applied Mathematics 17 Springer, New York (2002). (2002) Zbl1006.92001MR1908418
- Murray, J. D., Mathematical Biology, Vol. 2: Spatial Models and Biomedical Applications. 3rd revised ed, Interdisciplinary Applied Mathematics 18 Springer, New York (2003). (2003) Zbl1006.92002MR1952568
- Nindjin, A. F., Aziz-Alaoui, M. A., Cadivel, M., Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay, Nonlinear Anal., Real World Appl. 7 (2006), 1104-1118. (2006) Zbl1104.92065MR2260902
- Pao, C. V., 10.1006/jmaa.1996.0111, J. Math. Anal. Appl. 198 (1996), 751-779. (1996) Zbl0860.35138MR1377823DOI10.1006/jmaa.1996.0111
- Ryu, K., Ahn, I., 10.1016/j.jde.2005.06.020, J. Differ. Equations 218 (2005), 117-135. (2005) MR2174969DOI10.1016/j.jde.2005.06.020
- Tian, Y., Weng, P., 10.1007/s10440-011-9607-9, Acta Appl. Math. 114 (2011), 173-192. (2011) Zbl1216.35159MR2794080DOI10.1007/s10440-011-9607-9
- Upadhyay, R. K., Iyengar, S. R. K., Effect of seasonality on the dynamics of 2 and 3 species prey-predator systems, Nonlinear Anal., Real World Appl. 6 (2005), 509-530. (2005) Zbl1072.92058MR2129561
- Wang, Y.-M., 10.1016/j.jmaa.2006.05.020, J. Math. Anal. Appl. 328 (2007), 137-150. (2007) Zbl1112.35106MR2285539DOI10.1016/j.jmaa.2006.05.020
- Wang, W., Takeuchi, Y., Saito, Y., Nakaoka, S., 10.1016/j.jtbi.2005.12.008, J. Theoret. Biol. 241 (2006), 451-458. (2006) MR2254918DOI10.1016/j.jtbi.2005.12.008
- Wu, J., 10.1007/978-1-4612-4050-1, Applied Mathematical Sciences 119 Springer, New York (1996). (1996) Zbl0870.35116DOI10.1007/978-1-4612-4050-1
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.