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Clines with directional selection and partial panmixia in an unbounded unidimensional habitat
Traveling waves of a mutualistic model of mistletoes and birds
1. | Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China |
2. | Department of Mathematics and Department of Zoology and Physiology, University of Wyoming, Laramie, WY, 82071 |
3. | Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795 |
4. | Department of Zoology and Physiology, University of Wyoming, Laramie, WY, 82071, United States |
References:
[1] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math., 30 (1978), 33-76.
doi: 10.1016/0001-8708(78)90130-5. |
[2] |
J. E. Aukema, Vectors, viscin, and viscaceae: Mistletoes as parasites, mutualists, and resources, Front. Ecol. Environ., 1 (2003), 212-219. |
[3] |
J. E. Aukema and C. M. del Rio, Where does a fruit-eating bird deposit mistletoe seeds? seed deposition patterns and an experiment, Ecology, 83 (2002), 3489-3496.
doi: 10.2307/3072097. |
[4] |
J. Fang, J. Wei and X. Zhao, Spatial dynamics of a nonlocal and time-delayed reaction diffusion system, J. Differential Equations, 245 (2008), 2749-2770.
doi: 10.1016/j.jde.2008.09.001. |
[5] |
J. Fang and X. Zhao, Monotone wavefronts for partially degenerate reaction-diffusion systems, J. Dynam. Differential Equations, 21 (2009), 663-680.
doi: 10.1007/s10884-009-9152-7. |
[6] |
J. Fang and X. Zhao, Traveling waves for monotone semiflows with weak compactness,, SIAM J. Math. Anal., ().
|
[7] |
C. Gosper, C. D. Stansbury and G. Vivian-Smith, Seed dispersal of fleshy-fruited invasive plants by birds: Contributing factors and management options, Diversity and Distributions, 11 (2005), 549-558.
doi: 10.1111/j.1366-9516.2005.00195.x. |
[8] |
B. Li, Traveling wave solutions in partially degenerate cooperative reaction-diffusion systems, J. Differential Equations, 252 (2012), 4842-4861.
doi: 10.1016/j.jde.2012.01.018. |
[9] |
B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196 (2005), 82-98.
doi: 10.1016/j.mbs.2005.03.008. |
[10] |
B. Li and L. Zhang, Travelling wave solutions in delayed cooperative systems, Nonlinearity, 24 (2011), 1759-1776.
doi: 10.1088/0951-7715/24/6/004. |
[11] |
X. Liang and X. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[12] |
X. Liang and X. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857-903.
doi: 10.1016/j.jfa.2010.04.018. |
[13] |
G. Lin, W. Li and S. Ruan, Monostable wavefronts in cooperative Lotka-Volterra systems with nonlocal delays, Discrete Contin. Dyn. Syst., 31 (2011), 1-23.
doi: 10.3934/dcds.2011.31.1. |
[14] |
R. Liu, C. M. del Rio and J. Wu, Spatiotemporal variation of mistletoes: A dynamic modeling approach, Bull. Math. Biol., 73 (2011), 1794-1811.
doi: 10.1007/s11538-010-9592-6. |
[15] |
N. Reid, Coevolution of mistletoes and frugivorous birds, Australian Journal of Ecology, 16 (1991), 457-469.
doi: 10.1111/j.1442-9993.1991.tb01075.x. |
[16] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, vol. 41 of Mathematical Surveys and Monographs, Amer. Math. Soc., Providence, RI, 1995. |
[17] |
C. Wang, R. Liu, J. Shi and C. M. del Rio, Spatiotemporal mutualistic model of mistletoes and birds, J. Math. Biol., 68 (2014), 1479-1520.
doi: 10.1007/s00285-013-0664-8. |
[18] |
Z. Wang, W. Li and S. Ruan, Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay, J. Differential Equations, 238 (2007), 153-200.
doi: 10.1016/j.jde.2007.03.025. |
[19] |
Z. Wang, W. Li and S. Ruan, Traveling fronts in monostable equations with nonlocal delayed effects, J. Dynam. Differential Equations, 20 (2008), 573-607.
doi: 10.1007/s10884-008-9103-8. |
[20] |
H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.
doi: 10.1007/s00285-007-0078-6. |
[21] |
P. Weng and X. Zhao, Spreading speed and traveling waves for a multi-type {SIS} epidemic model, J. Differential Equations, 229 (2006), 270-296.
doi: 10.1016/j.jde.2006.01.020. |
[22] |
S. Wu, Y. Sun and S. Liu, Traveling fronts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity, Discrete Contin. Dyn. Syst., 33 (2013), 921-946.
doi: 10.3934/dcds.2013.33.921. |
[23] |
X. Zhao, Dynamical System in Population Biology, Springer, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
show all references
References:
[1] |
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math., 30 (1978), 33-76.
doi: 10.1016/0001-8708(78)90130-5. |
[2] |
J. E. Aukema, Vectors, viscin, and viscaceae: Mistletoes as parasites, mutualists, and resources, Front. Ecol. Environ., 1 (2003), 212-219. |
[3] |
J. E. Aukema and C. M. del Rio, Where does a fruit-eating bird deposit mistletoe seeds? seed deposition patterns and an experiment, Ecology, 83 (2002), 3489-3496.
doi: 10.2307/3072097. |
[4] |
J. Fang, J. Wei and X. Zhao, Spatial dynamics of a nonlocal and time-delayed reaction diffusion system, J. Differential Equations, 245 (2008), 2749-2770.
doi: 10.1016/j.jde.2008.09.001. |
[5] |
J. Fang and X. Zhao, Monotone wavefronts for partially degenerate reaction-diffusion systems, J. Dynam. Differential Equations, 21 (2009), 663-680.
doi: 10.1007/s10884-009-9152-7. |
[6] |
J. Fang and X. Zhao, Traveling waves for monotone semiflows with weak compactness,, SIAM J. Math. Anal., ().
|
[7] |
C. Gosper, C. D. Stansbury and G. Vivian-Smith, Seed dispersal of fleshy-fruited invasive plants by birds: Contributing factors and management options, Diversity and Distributions, 11 (2005), 549-558.
doi: 10.1111/j.1366-9516.2005.00195.x. |
[8] |
B. Li, Traveling wave solutions in partially degenerate cooperative reaction-diffusion systems, J. Differential Equations, 252 (2012), 4842-4861.
doi: 10.1016/j.jde.2012.01.018. |
[9] |
B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196 (2005), 82-98.
doi: 10.1016/j.mbs.2005.03.008. |
[10] |
B. Li and L. Zhang, Travelling wave solutions in delayed cooperative systems, Nonlinearity, 24 (2011), 1759-1776.
doi: 10.1088/0951-7715/24/6/004. |
[11] |
X. Liang and X. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[12] |
X. Liang and X. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857-903.
doi: 10.1016/j.jfa.2010.04.018. |
[13] |
G. Lin, W. Li and S. Ruan, Monostable wavefronts in cooperative Lotka-Volterra systems with nonlocal delays, Discrete Contin. Dyn. Syst., 31 (2011), 1-23.
doi: 10.3934/dcds.2011.31.1. |
[14] |
R. Liu, C. M. del Rio and J. Wu, Spatiotemporal variation of mistletoes: A dynamic modeling approach, Bull. Math. Biol., 73 (2011), 1794-1811.
doi: 10.1007/s11538-010-9592-6. |
[15] |
N. Reid, Coevolution of mistletoes and frugivorous birds, Australian Journal of Ecology, 16 (1991), 457-469.
doi: 10.1111/j.1442-9993.1991.tb01075.x. |
[16] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, vol. 41 of Mathematical Surveys and Monographs, Amer. Math. Soc., Providence, RI, 1995. |
[17] |
C. Wang, R. Liu, J. Shi and C. M. del Rio, Spatiotemporal mutualistic model of mistletoes and birds, J. Math. Biol., 68 (2014), 1479-1520.
doi: 10.1007/s00285-013-0664-8. |
[18] |
Z. Wang, W. Li and S. Ruan, Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay, J. Differential Equations, 238 (2007), 153-200.
doi: 10.1016/j.jde.2007.03.025. |
[19] |
Z. Wang, W. Li and S. Ruan, Traveling fronts in monostable equations with nonlocal delayed effects, J. Dynam. Differential Equations, 20 (2008), 573-607.
doi: 10.1007/s10884-008-9103-8. |
[20] |
H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.
doi: 10.1007/s00285-007-0078-6. |
[21] |
P. Weng and X. Zhao, Spreading speed and traveling waves for a multi-type {SIS} epidemic model, J. Differential Equations, 229 (2006), 270-296.
doi: 10.1016/j.jde.2006.01.020. |
[22] |
S. Wu, Y. Sun and S. Liu, Traveling fronts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity, Discrete Contin. Dyn. Syst., 33 (2013), 921-946.
doi: 10.3934/dcds.2013.33.921. |
[23] |
X. Zhao, Dynamical System in Population Biology, Springer, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
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