-
Previous Article
Coexistence and asymptotic stability in stage-structured predator-prey models
- MBE Home
- This Issue
-
Next Article
Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate
On a diffusive predator-prey model with nonlinear harvesting
1. | Department of Mathematics, Florida Gulf Coast University, 11501 FGCU Blvd. S., Fort Myers, FL 33965, United States |
References:
[1] |
M. A. Aziz-Alaoui, Study of a Leslie-Gower-type tritrophic population, Chaos Sol. and Fractals, 14 (2002), 1275-1293.
doi: 10.1016/S0960-0779(02)00079-6. |
[2] |
M. A. Aziz-Alaoui and M. Daher Okiye, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Appl. Math. Lett., 16 (2003), 1069-1075.
doi: 10.1016/S0893-9659(03)90096-6. |
[3] |
J. B. Collings, The effects of the functional response on the bifurcation behavior of a mite predator-prey interaction model, J. Math. Biol., 36 (1997), 149-168.
doi: 10.1007/s002850050095. |
[4] |
Y. Du, R. Peng and M. Wang, Effect of a protection zone in the diffusive Leslie predator-prey model, J. Diff. Eqns., 246 (2009), 3932-3956.
doi: 10.1016/j.jde.2008.11.007. |
[5] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New-York, 1983. |
[6] |
X. N. Guan, W. M. Wang and Y. L. Cai, Spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge, Nonlinear Analysis: Real World Applications, 12 (2011), 2385-2395.
doi: 10.1016/j.nonrwa.2011.02.011. |
[7] |
R. P. Gupta and P Chandra, Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting, J. Math. Anal. Appl., 398 (2013), 278-295.
doi: 10.1016/j.jmaa.2012.08.057. |
[8] |
A. Korobeinikov, A Lyapunov function for Leslie-Gower predator-prey models, Appl. Math. Lett., 14 (2011), 697-699.
doi: 10.1016/S0893-9659(01)80029-X. |
[9] |
T. K. Kar, Modelling and analysis of a harvested prey-predator system incorporating a prey refuge, J. Comput. Appl Math., 185 (2006), 19-33.
doi: 10.1016/j.cam.2005.01.035. |
[10] |
B. Leard, C. Lewis and J. Rebaza, Dynamics of ratio-dependent predator-prey models with nonconstant harvesting, Disc. Cont. Dyn. Syst. S, 1 (2008), 303-315.
doi: 10.3934/dcdss.2008.1.303. |
[11] |
P. H. Leslie, Some further notes on the use of matrices on population mathematics, Biometrika, 35 (1948), 213-245. |
[12] |
R. M. May, Stability and Complexity in Model Ecosystem, Princeton University Press, Princeton, NJ, 1974. |
[13] |
A. F. Nindjin, M. A. Aziz-Alaoui and M. Cadivel, 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.
doi: 10.1016/j.nonrwa.2005.10.003. |
[14] |
D. J. Wollkind, J. B. Collings and J. A. Logan, Metastability in a temperature-dependent model system for predator-prey mite outbreak interactions on fruit trees, Bull. Math. Biol., 50 (1988), 379-409.
doi: 10.1007/BF02459707. |
[15] |
D. Xiao, W. Li and M. Han, Dynamics in a ratio-dependent predator-prey model with predator harvesting, J. Math. Anal and Appl., 324 (2006), 14-29.
doi: 10.1016/j.jmaa.2005.11.048. |
[16] |
Q. Ye and Z. Li, Introduction to Reaction-Diffusion Equations, Science Press, Beijing, 1990. |
[17] |
N. Zhang, F. D. Chen, Q. Q. Su and T. Wu, Dynamic behaviors of a harvesting Leslie-Gower predator-prey model, Discrete Dyn. Nat. Soc., (2011), Art. ID 473949, 14 pp.
doi: 10.1155/2011/473949. |
[18] |
Y. Zhu and K. Wang, Existence and global attractivity of positive periodic solutions for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, J. Math. Anal. Appl., 384 (2011), 400-408.
doi: 10.1016/j.jmaa.2011.05.081. |
show all references
References:
[1] |
M. A. Aziz-Alaoui, Study of a Leslie-Gower-type tritrophic population, Chaos Sol. and Fractals, 14 (2002), 1275-1293.
doi: 10.1016/S0960-0779(02)00079-6. |
[2] |
M. A. Aziz-Alaoui and M. Daher Okiye, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Appl. Math. Lett., 16 (2003), 1069-1075.
doi: 10.1016/S0893-9659(03)90096-6. |
[3] |
J. B. Collings, The effects of the functional response on the bifurcation behavior of a mite predator-prey interaction model, J. Math. Biol., 36 (1997), 149-168.
doi: 10.1007/s002850050095. |
[4] |
Y. Du, R. Peng and M. Wang, Effect of a protection zone in the diffusive Leslie predator-prey model, J. Diff. Eqns., 246 (2009), 3932-3956.
doi: 10.1016/j.jde.2008.11.007. |
[5] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New-York, 1983. |
[6] |
X. N. Guan, W. M. Wang and Y. L. Cai, Spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge, Nonlinear Analysis: Real World Applications, 12 (2011), 2385-2395.
doi: 10.1016/j.nonrwa.2011.02.011. |
[7] |
R. P. Gupta and P Chandra, Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting, J. Math. Anal. Appl., 398 (2013), 278-295.
doi: 10.1016/j.jmaa.2012.08.057. |
[8] |
A. Korobeinikov, A Lyapunov function for Leslie-Gower predator-prey models, Appl. Math. Lett., 14 (2011), 697-699.
doi: 10.1016/S0893-9659(01)80029-X. |
[9] |
T. K. Kar, Modelling and analysis of a harvested prey-predator system incorporating a prey refuge, J. Comput. Appl Math., 185 (2006), 19-33.
doi: 10.1016/j.cam.2005.01.035. |
[10] |
B. Leard, C. Lewis and J. Rebaza, Dynamics of ratio-dependent predator-prey models with nonconstant harvesting, Disc. Cont. Dyn. Syst. S, 1 (2008), 303-315.
doi: 10.3934/dcdss.2008.1.303. |
[11] |
P. H. Leslie, Some further notes on the use of matrices on population mathematics, Biometrika, 35 (1948), 213-245. |
[12] |
R. M. May, Stability and Complexity in Model Ecosystem, Princeton University Press, Princeton, NJ, 1974. |
[13] |
A. F. Nindjin, M. A. Aziz-Alaoui and M. Cadivel, 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.
doi: 10.1016/j.nonrwa.2005.10.003. |
[14] |
D. J. Wollkind, J. B. Collings and J. A. Logan, Metastability in a temperature-dependent model system for predator-prey mite outbreak interactions on fruit trees, Bull. Math. Biol., 50 (1988), 379-409.
doi: 10.1007/BF02459707. |
[15] |
D. Xiao, W. Li and M. Han, Dynamics in a ratio-dependent predator-prey model with predator harvesting, J. Math. Anal and Appl., 324 (2006), 14-29.
doi: 10.1016/j.jmaa.2005.11.048. |
[16] |
Q. Ye and Z. Li, Introduction to Reaction-Diffusion Equations, Science Press, Beijing, 1990. |
[17] |
N. Zhang, F. D. Chen, Q. Q. Su and T. Wu, Dynamic behaviors of a harvesting Leslie-Gower predator-prey model, Discrete Dyn. Nat. Soc., (2011), Art. ID 473949, 14 pp.
doi: 10.1155/2011/473949. |
[18] |
Y. Zhu and K. Wang, Existence and global attractivity of positive periodic solutions for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, J. Math. Anal. Appl., 384 (2011), 400-408.
doi: 10.1016/j.jmaa.2011.05.081. |
[1] |
Changrong Zhu, Lei Kong. Bifurcations analysis of Leslie-Gower predator-prey models with nonlinear predator-harvesting. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1187-1206. doi: 10.3934/dcdss.2017065 |
[2] |
Yong Yao, Lingling Liu. Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021252 |
[3] |
C. R. Zhu, K. Q. Lan. Phase portraits, Hopf bifurcations and limit cycles of Leslie-Gower predator-prey systems with harvesting rates. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 289-306. doi: 10.3934/dcdsb.2010.14.289 |
[4] |
Yunfeng Liu, Zhiming Guo, Mohammad El Smaily, Lin Wang. A Leslie-Gower predator-prey model with a free boundary. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2063-2084. doi: 10.3934/dcdss.2019133 |
[5] |
Hongmei Cheng, Rong Yuan. Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5433-5454. doi: 10.3934/dcds.2017236 |
[6] |
Zengji Du, Xiao Chen, Zhaosheng Feng. Multiple positive periodic solutions to a predator-prey model with Leslie-Gower Holling-type II functional response and harvesting terms. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1203-1214. doi: 10.3934/dcdss.2014.7.1203 |
[7] |
Walid Abid, Radouane Yafia, M.A. Aziz-Alaoui, Habib Bouhafa, Azgal Abichou. Global dynamics on a circular domain of a diffusion predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional type. Evolution Equations and Control Theory, 2015, 4 (2) : 115-129. doi: 10.3934/eect.2015.4.115 |
[8] |
Hongwei Yin, Xiaoyong Xiao, Xiaoqing Wen. Analysis of a Lévy-diffusion Leslie-Gower predator-prey model with nonmonotonic functional response. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2121-2151. doi: 10.3934/dcdsb.2018228 |
[9] |
Jun Zhou. Qualitative analysis of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses. Communications on Pure and Applied Analysis, 2015, 14 (3) : 1127-1145. doi: 10.3934/cpaa.2015.14.1127 |
[10] |
Rong Zou, Shangjiang Guo. Dynamics of a diffusive Leslie-Gower predator-prey model in spatially heterogeneous environment. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4189-4210. doi: 10.3934/dcdsb.2020093 |
[11] |
Baifeng Zhang, Guohong Zhang, Xiaoli Wang. Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021260 |
[12] |
Shiwen Niu, Hongmei Cheng, Rong Yuan. A free boundary problem of some modified Leslie-Gower predator-prey model with nonlocal diffusion term. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2189-2219. doi: 10.3934/dcdsb.2021129 |
[13] |
Jun Zhou, Chan-Gyun Kim, Junping Shi. Positive steady state solutions of a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3875-3899. doi: 10.3934/dcds.2014.34.3875 |
[14] |
Wenjie Ni, Mingxin Wang. Dynamical properties of a Leslie-Gower prey-predator model with strong Allee effect in prey. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3409-3420. doi: 10.3934/dcdsb.2017172 |
[15] |
Safia Slimani, Paul Raynaud de Fitte, Islam Boussaada. Dynamics of a prey-predator system with modified Leslie-Gower and Holling type Ⅱ schemes incorporating a prey refuge. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 5003-5039. doi: 10.3934/dcdsb.2019042 |
[16] |
Na Min, Mingxin Wang. Hopf bifurcation and steady-state bifurcation for a Leslie-Gower prey-predator model with strong Allee effect in prey. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1071-1099. doi: 10.3934/dcds.2019045 |
[17] |
Jinfeng Wang, Sainan Wu, Junping Shi. Pattern formation in diffusive predator-prey systems with predator-taxis and prey-taxis. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1273-1289. doi: 10.3934/dcdsb.2020162 |
[18] |
Zhifu Xie. Turing instability in a coupled predator-prey model with different Holling type functional responses. Discrete and Continuous Dynamical Systems - S, 2011, 4 (6) : 1621-1628. doi: 10.3934/dcdss.2011.4.1621 |
[19] |
Wei Feng, Jody Hinson. Stability and pattern in two-patch predator-prey population dynamics. Conference Publications, 2005, 2005 (Special) : 268-279. doi: 10.3934/proc.2005.2005.268 |
[20] |
Xiaoying Wang, Xingfu Zou. Pattern formation of a predator-prey model with the cost of anti-predator behaviors. Mathematical Biosciences & Engineering, 2018, 15 (3) : 775-805. doi: 10.3934/mbe.2018035 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]