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Neimark-Sacker bifurcations in a host-parasitoid system with a host refuge
1. | Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan |
2. | Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States |
References:
[1] |
L. J. S. Allen, An Introduction to Mathematical Biology, Prentice-Hall, New Jersey, 2006. |
[2] |
M. Begon, J. Harper and C. Townsend, Ecology: Individuals, Populations and Communities, Blackwell Science Ltd, New York, 1996. |
[3] |
F. Berezovskaya, B. Song and C. Castillo-Chavez, Role of prey dispersal and refuges on predator-prey dynamics, SIAM J. Appl. Math., 70 (2010), 1821-1839.
doi: 10.1137/080730603. |
[4] |
G. Butler and P. Waltman, Persistence in dynamical systems, J. Diff. Equ., 63 (1986), 255-263.
doi: 10.1016/0022-0396(86)90049-5. |
[5] |
E. Gonzalez-Olivares and R. Ramos-Jiliberto, Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability, Ecol. Model., 166 (2003), 135-146.
doi: 10.1016/S0304-3800(03)00131-5. |
[6] |
J. K. Hale and H. Koçak, Dynamics and Bifurcations, Springer, New York, 1991.
doi: 10.1007/978-1-4612-4426-4. |
[7] |
M. P. Hassell, The Dynamics of Arthropod Predator-Prey Systems, Princeton Univeristy Press, Princeton, New Jersey, 1978. |
[8] |
A. Hines and J. Pearse, Abalones, shells, and sea otters: Dynamics of prey populations in central California, Ecol., 63 (1982), 1547-1560.
doi: 10.2307/1938879. |
[9] |
J. Hofbauer and J. So, Uniform persistence and repellors for maps, Proc. Am. Math. Soc., 107 (1989), 1137-1142.
doi: 10.1090/S0002-9939-1989-0984816-4. |
[10] |
Y. Huang, F. Chen and Z. Li, Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge, App. Math. Comput., 182 (2006), 672-683.
doi: 10.1016/j.amc.2006.04.030. |
[11] |
V. Hutson, A theorem on average Liapunov functions, Monash. Math., 98 (1984), 267-275.
doi: 10.1007/BF01540776. |
[12] |
S. R.-J. Jang, Allee effects in a discrete-time host-parasitoid model, J. Difference Equ. Appl., 12 (2006), 165-181.
doi: 10.1080/10236190500539238. |
[13] |
L. Ji and C. Wu, Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge, Nonl. Ana.: RWA, 11 (2010), 2285-2295.
doi: 10.1016/j.nonrwa.2009.07.003. |
[14] |
V. Krivan, Behavioral refuges and predator-prey coexistence, J. Theo. Biol., 339 (2013), 112-121.
doi: 10.1016/j.jtbi.2012.12.016. |
[15] |
Z. Ma, W. Li, Y. Zhao, W. Wang, H. Zhang and Z. Li, Effects of prey refuges on a predator-prey model with a class of functional responses: The role of refuges, Math. Biosci., 218 (2009), 73-79.
doi: 10.1016/j.mbs.2008.12.008. |
[16] |
J. Maynard Smith, Models in Ecology, Cambridge Univ. Press, London, 1974. |
[17] |
J. McNair, The effects of refuges on predator-prey interactions: A reconsideration, Theo. Pop. Biol., 29 (1986), 38-63.
doi: 10.1016/0040-5809(86)90004-3. |
[18] |
J. McNair, Stability effects of prey refuges with entry-exit dynamics, J. Theor. Biol., 125 (1987), 449-464.
doi: 10.1016/S0022-5193(87)80213-8. |
[19] |
W. Murdoch and A. Oaten, Predation and population stability, Adv. Ecol. Res., 9 (1975), 1-131.
doi: 10.1016/S0065-2504(08)60288-3. |
[20] |
A. Sih, Prey refuges and predator-prey stability, Theo. Pop. Biol., 31 (1987), 1-12.
doi: 10.1016/0040-5809(87)90019-0. |
[21] |
R. Taylor, Predation, Chapman and Hall, New York, 1984.
doi: 10.1007/978-94-009-5554-7. |
[22] |
S. Woodin, Refuges, disturbance, and community structure: A marine soft-bottom example, Ecol., 59 (1978), 274-284.
doi: 10.2307/1936373. |
[23] |
S. Woodin, Disturbance and community structure in a shallow water sand flat, Ecol., 62 (1981), 1052-1066.
doi: 10.2307/1937004. |
show all references
References:
[1] |
L. J. S. Allen, An Introduction to Mathematical Biology, Prentice-Hall, New Jersey, 2006. |
[2] |
M. Begon, J. Harper and C. Townsend, Ecology: Individuals, Populations and Communities, Blackwell Science Ltd, New York, 1996. |
[3] |
F. Berezovskaya, B. Song and C. Castillo-Chavez, Role of prey dispersal and refuges on predator-prey dynamics, SIAM J. Appl. Math., 70 (2010), 1821-1839.
doi: 10.1137/080730603. |
[4] |
G. Butler and P. Waltman, Persistence in dynamical systems, J. Diff. Equ., 63 (1986), 255-263.
doi: 10.1016/0022-0396(86)90049-5. |
[5] |
E. Gonzalez-Olivares and R. Ramos-Jiliberto, Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability, Ecol. Model., 166 (2003), 135-146.
doi: 10.1016/S0304-3800(03)00131-5. |
[6] |
J. K. Hale and H. Koçak, Dynamics and Bifurcations, Springer, New York, 1991.
doi: 10.1007/978-1-4612-4426-4. |
[7] |
M. P. Hassell, The Dynamics of Arthropod Predator-Prey Systems, Princeton Univeristy Press, Princeton, New Jersey, 1978. |
[8] |
A. Hines and J. Pearse, Abalones, shells, and sea otters: Dynamics of prey populations in central California, Ecol., 63 (1982), 1547-1560.
doi: 10.2307/1938879. |
[9] |
J. Hofbauer and J. So, Uniform persistence and repellors for maps, Proc. Am. Math. Soc., 107 (1989), 1137-1142.
doi: 10.1090/S0002-9939-1989-0984816-4. |
[10] |
Y. Huang, F. Chen and Z. Li, Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge, App. Math. Comput., 182 (2006), 672-683.
doi: 10.1016/j.amc.2006.04.030. |
[11] |
V. Hutson, A theorem on average Liapunov functions, Monash. Math., 98 (1984), 267-275.
doi: 10.1007/BF01540776. |
[12] |
S. R.-J. Jang, Allee effects in a discrete-time host-parasitoid model, J. Difference Equ. Appl., 12 (2006), 165-181.
doi: 10.1080/10236190500539238. |
[13] |
L. Ji and C. Wu, Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge, Nonl. Ana.: RWA, 11 (2010), 2285-2295.
doi: 10.1016/j.nonrwa.2009.07.003. |
[14] |
V. Krivan, Behavioral refuges and predator-prey coexistence, J. Theo. Biol., 339 (2013), 112-121.
doi: 10.1016/j.jtbi.2012.12.016. |
[15] |
Z. Ma, W. Li, Y. Zhao, W. Wang, H. Zhang and Z. Li, Effects of prey refuges on a predator-prey model with a class of functional responses: The role of refuges, Math. Biosci., 218 (2009), 73-79.
doi: 10.1016/j.mbs.2008.12.008. |
[16] |
J. Maynard Smith, Models in Ecology, Cambridge Univ. Press, London, 1974. |
[17] |
J. McNair, The effects of refuges on predator-prey interactions: A reconsideration, Theo. Pop. Biol., 29 (1986), 38-63.
doi: 10.1016/0040-5809(86)90004-3. |
[18] |
J. McNair, Stability effects of prey refuges with entry-exit dynamics, J. Theor. Biol., 125 (1987), 449-464.
doi: 10.1016/S0022-5193(87)80213-8. |
[19] |
W. Murdoch and A. Oaten, Predation and population stability, Adv. Ecol. Res., 9 (1975), 1-131.
doi: 10.1016/S0065-2504(08)60288-3. |
[20] |
A. Sih, Prey refuges and predator-prey stability, Theo. Pop. Biol., 31 (1987), 1-12.
doi: 10.1016/0040-5809(87)90019-0. |
[21] |
R. Taylor, Predation, Chapman and Hall, New York, 1984.
doi: 10.1007/978-94-009-5554-7. |
[22] |
S. Woodin, Refuges, disturbance, and community structure: A marine soft-bottom example, Ecol., 59 (1978), 274-284.
doi: 10.2307/1936373. |
[23] |
S. Woodin, Disturbance and community structure in a shallow water sand flat, Ecol., 62 (1981), 1052-1066.
doi: 10.2307/1937004. |
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