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Global dynamics of three species omnivory models with Lotka-Volterra interaction
1. | Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137 |
2. | Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China |
3. | Department of Mathematics, Tamkang University, Tamsui, New Taipei City 25137, Taiwan |
References:
[1] |
G. Butler, H. I. Freedman and P. Waltman, Uniformly persistent systems, Proceedings of the American Mathematical Society, 96 (1986), 425-430.
doi: 10.1090/S0002-9939-1986-0822433-4. |
[2] |
H. I. Freedman, S. G. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set, Journal of Dynamics and Differential Equations, 6 (1994), 583-600.
doi: 10.1007/BF02218848. |
[3] |
H. I. Freedman and P. Waltman, Persistence in models of three interacting predator-prey populations, Mathematical Biosciences, 68 (1984), 213-231.
doi: 10.1016/0025-5564(84)90032-4. |
[4] |
R. D. Holt, Predation, apparent competition and the structure of prey communities, Theoretical Population Biology. An International Journal, 12 (1977), 197-229.
doi: 10.1016/0040-5809(77)90042-9. |
[5] |
R. D. Holt and J. H. Lawton, The Ecological Consequences of Shared Natural Enemies, Annual Review of Ecology and Systematics, 25 (1994), 495-520.
doi: 10.1146/annurev.es.25.110194.002431. |
[6] |
R. D. Holt and G. A. Polis, A theoretical framework for intraguild predation, American Naturalist, 149 (1997), 745-764.
doi: 10.1086/286018. |
[7] |
S.-B. Hsu, S. Ruan and T.-H. Yang, Analysis of three species Lotka-Volterra food web models with omnivory, Journal of Mathematical Analysis and Applications, 426 (2015), 659-687.
doi: 10.1016/j.jmaa.2015.01.035. |
[8] |
Y. Kang and L. Wedekin, Dynamics of a intraguild predation model with generalist or specialist predator, Journal of Mathematical Biology, 67 (2013), 1227-1259.
doi: 10.1007/s00285-012-0584-z. |
[9] |
N. Krikorian, The Volterra model for three species predator-prey systems: Boundedness and stability, Journal of Mathematical Biology, 7 (1979), 117-132.
doi: 10.1007/BF00276925. |
[10] |
T. Namba and K. Tanabe, Omnivory and stability of food webs, Ecological Complexity, 5 (2008), 73-85.
doi: 10.1016/j.ecocom.2008.02.001. |
[11] |
E. R. Pianka, On $r$- and $K$-selection, American Naturalist, 104 (1970), 592-597.
doi: 10.1086/282697. |
[12] |
J. Vandermeer, Omnivory and the stability of food webs, Journal of Theoretical Biology, 238 (2006), 497-504.
doi: 10.1016/j.jtbi.2005.06.006. |
[13] |
S.-R. Zhou, W.-T. Li and G. Wang, Persistence and global stability of positive periodic solutions of three species food chains with omnivory, Journal of Mathematical Analysis and Applications, 324 (2006), 397-408.
doi: 10.1016/j.jmaa.2005.12.021. |
show all references
References:
[1] |
G. Butler, H. I. Freedman and P. Waltman, Uniformly persistent systems, Proceedings of the American Mathematical Society, 96 (1986), 425-430.
doi: 10.1090/S0002-9939-1986-0822433-4. |
[2] |
H. I. Freedman, S. G. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set, Journal of Dynamics and Differential Equations, 6 (1994), 583-600.
doi: 10.1007/BF02218848. |
[3] |
H. I. Freedman and P. Waltman, Persistence in models of three interacting predator-prey populations, Mathematical Biosciences, 68 (1984), 213-231.
doi: 10.1016/0025-5564(84)90032-4. |
[4] |
R. D. Holt, Predation, apparent competition and the structure of prey communities, Theoretical Population Biology. An International Journal, 12 (1977), 197-229.
doi: 10.1016/0040-5809(77)90042-9. |
[5] |
R. D. Holt and J. H. Lawton, The Ecological Consequences of Shared Natural Enemies, Annual Review of Ecology and Systematics, 25 (1994), 495-520.
doi: 10.1146/annurev.es.25.110194.002431. |
[6] |
R. D. Holt and G. A. Polis, A theoretical framework for intraguild predation, American Naturalist, 149 (1997), 745-764.
doi: 10.1086/286018. |
[7] |
S.-B. Hsu, S. Ruan and T.-H. Yang, Analysis of three species Lotka-Volterra food web models with omnivory, Journal of Mathematical Analysis and Applications, 426 (2015), 659-687.
doi: 10.1016/j.jmaa.2015.01.035. |
[8] |
Y. Kang and L. Wedekin, Dynamics of a intraguild predation model with generalist or specialist predator, Journal of Mathematical Biology, 67 (2013), 1227-1259.
doi: 10.1007/s00285-012-0584-z. |
[9] |
N. Krikorian, The Volterra model for three species predator-prey systems: Boundedness and stability, Journal of Mathematical Biology, 7 (1979), 117-132.
doi: 10.1007/BF00276925. |
[10] |
T. Namba and K. Tanabe, Omnivory and stability of food webs, Ecological Complexity, 5 (2008), 73-85.
doi: 10.1016/j.ecocom.2008.02.001. |
[11] |
E. R. Pianka, On $r$- and $K$-selection, American Naturalist, 104 (1970), 592-597.
doi: 10.1086/282697. |
[12] |
J. Vandermeer, Omnivory and the stability of food webs, Journal of Theoretical Biology, 238 (2006), 497-504.
doi: 10.1016/j.jtbi.2005.06.006. |
[13] |
S.-R. Zhou, W.-T. Li and G. Wang, Persistence and global stability of positive periodic solutions of three species food chains with omnivory, Journal of Mathematical Analysis and Applications, 324 (2006), 397-408.
doi: 10.1016/j.jmaa.2005.12.021. |
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