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A boundary value problem for integrodifference population models with cyclic kernels
1. | Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States |
2. | Department of Mathematics, University of Texas, Austin, TX 78712, United States |
References:
[1] |
C. J. Collins, C. I. Fraser, A. Ashcroft and J. M. Waters, Asymmetric dispersal of southern bull-kelp (Durvillaea antarctica) adults in coastal New Zealand: Testing and oceanographic hypothesis, Molecular Ecology, 19 (2010), 4572-4580.
doi: 10.1111/j.1365-294X.2010.04842.x. |
[2] |
R. Dirzo and P. H. Raven, Global state of biodiversity and loss, Annual Review of Environment and Resources, 28 (2003), 137-167. |
[3] |
N.-E. Fahssi, Polynomial triangles revisited. arXiv:1202.0228v7 [math.CO], (2012). |
[4] |
D. P. Hardin, P. Takáč and G. F. Webb, Asymptotic properties of a continuous-space discrete-time population model in a random environment, Journal of Mathematical Biology, 26 (1988), 361-374.
doi: 10.1007/BF00276367. |
[5] |
M. P. Hassel, The Dynamics of Arthropod Predator-Prey Systems, no. 13 in Monographs in Population Biology, Princeton University Press, 1978. |
[6] |
C. M. Herrera, P. Jordano, J. Guitian and A. Traveset, Annual variability in seed production by woody plants and the masting concept: Reassessment of principles and relationship to pollination and seed dispersal, The American Naturalist, 152 (1998), 576-594.
doi: 10.1086/286191. |
[7] |
H. F. Howe and J. Smallwood, Ecology of seed dispersal, Annual Review of Ecology and Systematics, 13 (1982), 201-228.
doi: 10.1146/annurev.es.13.110182.001221. |
[8] |
J. Jacobsen, Y. Jin, and M. A. Lewis, Integrodifference models for persistence in temporally varying river environments, preprint.
doi: 10.1007/s00285-014-0774-y. |
[9] |
M. Kot and W. M. Schaffer, Discrete-time growth-dispersal models, Mathematical Biosciences, 80 (1986), 109-136.
doi: 10.1016/0025-5564(86)90069-6. |
[10] |
M. A. Krasnosel'skii, Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964. |
[11] |
F. Lutscher, E. Pachepsky and M. A. Lewis, The effect of dispersal patterns on stream populations, SIAM Review, 47 (2005), 749-772.
doi: 10.1137/050636152. |
[12] |
M. G. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern-formation in a discrete-time predator-prey model, Theoretical Population Biology, 48 (1995), 7-43.
doi: 10.1006/tpbi.1995.1020. |
[13] |
D. Pearce, An economic approach to saving the tropical forests, in Economic Policy Towards the Environment, (ed. D. Helm), Blackwell Publishers, 1991, 239-262. |
[14] |
N. J. A. Sloane, Online Encyclopedia of Integer Sequences, 2013. |
[15] |
C. Tudge, Last Animals at the Zoo: How Mass Extinction Can Be Stopped, Island Press, Washington, D.C., 1992. |
[16] |
R. W. Van Kirk and M. A. Lewis, Integrodifference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107-137. |
show all references
References:
[1] |
C. J. Collins, C. I. Fraser, A. Ashcroft and J. M. Waters, Asymmetric dispersal of southern bull-kelp (Durvillaea antarctica) adults in coastal New Zealand: Testing and oceanographic hypothesis, Molecular Ecology, 19 (2010), 4572-4580.
doi: 10.1111/j.1365-294X.2010.04842.x. |
[2] |
R. Dirzo and P. H. Raven, Global state of biodiversity and loss, Annual Review of Environment and Resources, 28 (2003), 137-167. |
[3] |
N.-E. Fahssi, Polynomial triangles revisited. arXiv:1202.0228v7 [math.CO], (2012). |
[4] |
D. P. Hardin, P. Takáč and G. F. Webb, Asymptotic properties of a continuous-space discrete-time population model in a random environment, Journal of Mathematical Biology, 26 (1988), 361-374.
doi: 10.1007/BF00276367. |
[5] |
M. P. Hassel, The Dynamics of Arthropod Predator-Prey Systems, no. 13 in Monographs in Population Biology, Princeton University Press, 1978. |
[6] |
C. M. Herrera, P. Jordano, J. Guitian and A. Traveset, Annual variability in seed production by woody plants and the masting concept: Reassessment of principles and relationship to pollination and seed dispersal, The American Naturalist, 152 (1998), 576-594.
doi: 10.1086/286191. |
[7] |
H. F. Howe and J. Smallwood, Ecology of seed dispersal, Annual Review of Ecology and Systematics, 13 (1982), 201-228.
doi: 10.1146/annurev.es.13.110182.001221. |
[8] |
J. Jacobsen, Y. Jin, and M. A. Lewis, Integrodifference models for persistence in temporally varying river environments, preprint.
doi: 10.1007/s00285-014-0774-y. |
[9] |
M. Kot and W. M. Schaffer, Discrete-time growth-dispersal models, Mathematical Biosciences, 80 (1986), 109-136.
doi: 10.1016/0025-5564(86)90069-6. |
[10] |
M. A. Krasnosel'skii, Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964. |
[11] |
F. Lutscher, E. Pachepsky and M. A. Lewis, The effect of dispersal patterns on stream populations, SIAM Review, 47 (2005), 749-772.
doi: 10.1137/050636152. |
[12] |
M. G. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern-formation in a discrete-time predator-prey model, Theoretical Population Biology, 48 (1995), 7-43.
doi: 10.1006/tpbi.1995.1020. |
[13] |
D. Pearce, An economic approach to saving the tropical forests, in Economic Policy Towards the Environment, (ed. D. Helm), Blackwell Publishers, 1991, 239-262. |
[14] |
N. J. A. Sloane, Online Encyclopedia of Integer Sequences, 2013. |
[15] |
C. Tudge, Last Animals at the Zoo: How Mass Extinction Can Be Stopped, Island Press, Washington, D.C., 1992. |
[16] |
R. W. Van Kirk and M. A. Lewis, Integrodifference models for persistence in fragmented habitats, Bulletin of Mathematical Biology, 59 (1997), 107-137. |
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