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A boundary value problem for integrodifference population models with cyclic kernels
Persistence and extinction of diffusing populations with two sexes and short reproductive season
1. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, United States |
2. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 |
References:
[1] |
A. C. Ashih and W. G. Wilson, Two-sex population dynamics in space: Effects of gestation time on persistence, Theor. Pop. Biol., 60 (2001), 93-106.
doi: 10.1006/tpbi.2001.1527. |
[2] |
F. F. Bonsall, Linear operators in complete positive cones, Proc. London Math. Soc., 8 (1958), 53-75. |
[3] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley, Chichester, 2003.
doi: 10.1002/0470871296. |
[4] |
R. S. Cantrell, C. Cosner and Y. Lou, Advection-mediated coexistence of competing species, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), 497-518.
doi: 10.1017/S0308210506000047. |
[5] |
O. Diekmann, J. A. P. Heesterbeek and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Princeton University Press, Princeton, 2013. |
[6] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[7] |
K. P. Hadeler, Pair formation in age-structured populations, Acta Appl. Math., 14 (1989), 91-102.
doi: 10.1007/BF00046676. |
[8] |
M. Iannelli, M. Martcheva and F. A. Milner, Gender-Structured Population Models: Mathematical Methods, Numerics, and Simulations, SIAM, Philadelphia, 2005.
doi: 10.1137/1.9780898717488. |
[9] |
M. A. Krasnosel'skij, Positive Solutions of Operator Equations, Noordhoff, Groningen 1964. |
[10] |
M. A. Krasnosel'skij, Je. A. Lifshits and A. V. Sobolev, Positive Linear Systems: The Method of Positive Operators, Heldermann Verlag, Berlin, 1989. |
[11] |
B. Lemmens and R. D. Nussbaum, Nonlinear Perron-Frobenius Theory, Cambridge University Press, Cambridge, 2012.
doi: 10.1017/CBO9781139026079. |
[12] |
B. Lemmens and R. D. Nussbaum, Continuity of the cone spectral radius, Proc. Amer. Math. Soc., 141 (2013), 2741-2754.
doi: 10.1090/S0002-9939-2013-11520-0. |
[13] |
M. A. Lewis and B. Li, Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models, Bull. Math. Biol., 74 (2012), 2383-2402.
doi: 10.1007/s11538-012-9757-6. |
[14] |
J. Mallet-Paret and R. D. Nussbaum, Eigenvalues for a class of homogeneous cone maps arising from max-plus operators, Discr. Cont. Dyn. Sys. (DCDS-A), 8 (2002), 519-562.
doi: 10.3934/dcds.2002.8.519. |
[15] |
J. Mallet-Paret and R. D. Nussbaum, Generalizing the Krein-Rutman theorem, measures of noncompactness and the fixed point index, J. Fixed Point Theory and Appl., 7 (2010), 103-143.
doi: 10.1007/s11784-010-0010-3. |
[16] |
T. E. X. Miller, A. K. Shaw, B. D. Inouye and M. G. Neubert, Sex-biased dispersal and the speed of two-sex invasions, Amer. Nat., 177 (2011), 549-561.
doi: 10.1086/659628. |
[17] |
R. D. Nussbaum, Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem, Fixed Point Theory, (eds. E. Fadell and G. Fournier), Springer, Berlin New York, (1981), 309-331. |
[18] |
R. D. Nussbaum, Eigenvectors of order-preserving linear operators, J. London Math. Soc., 2 (1998), 480-496.
doi: 10.1112/S0024610798006425. |
[19] |
H. H. Schaefer, Halbgeordnete lokalkonvexe Vektorräume. II, Math. Ann., 138 (1959), 259-286.
doi: 10.1007/BF01342907. |
[20] |
H. H. Schaefer, Topological Vector Spaces, Macmillan, New York, 1966. |
[21] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Amer. Math. Soc., Providence, 1995. |
[22] |
H. L. Smith and H. R. Thieme, Dynamical Systems and Population Persistence, AMS, Providence, 2011 |
[23] |
H. R. Thieme, Eigenvectors and eigenfunctionals of homogeneous order-preserving maps, preprint, arXiv:1302.3905. |
[24] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
show all references
References:
[1] |
A. C. Ashih and W. G. Wilson, Two-sex population dynamics in space: Effects of gestation time on persistence, Theor. Pop. Biol., 60 (2001), 93-106.
doi: 10.1006/tpbi.2001.1527. |
[2] |
F. F. Bonsall, Linear operators in complete positive cones, Proc. London Math. Soc., 8 (1958), 53-75. |
[3] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley, Chichester, 2003.
doi: 10.1002/0470871296. |
[4] |
R. S. Cantrell, C. Cosner and Y. Lou, Advection-mediated coexistence of competing species, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), 497-518.
doi: 10.1017/S0308210506000047. |
[5] |
O. Diekmann, J. A. P. Heesterbeek and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Princeton University Press, Princeton, 2013. |
[6] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[7] |
K. P. Hadeler, Pair formation in age-structured populations, Acta Appl. Math., 14 (1989), 91-102.
doi: 10.1007/BF00046676. |
[8] |
M. Iannelli, M. Martcheva and F. A. Milner, Gender-Structured Population Models: Mathematical Methods, Numerics, and Simulations, SIAM, Philadelphia, 2005.
doi: 10.1137/1.9780898717488. |
[9] |
M. A. Krasnosel'skij, Positive Solutions of Operator Equations, Noordhoff, Groningen 1964. |
[10] |
M. A. Krasnosel'skij, Je. A. Lifshits and A. V. Sobolev, Positive Linear Systems: The Method of Positive Operators, Heldermann Verlag, Berlin, 1989. |
[11] |
B. Lemmens and R. D. Nussbaum, Nonlinear Perron-Frobenius Theory, Cambridge University Press, Cambridge, 2012.
doi: 10.1017/CBO9781139026079. |
[12] |
B. Lemmens and R. D. Nussbaum, Continuity of the cone spectral radius, Proc. Amer. Math. Soc., 141 (2013), 2741-2754.
doi: 10.1090/S0002-9939-2013-11520-0. |
[13] |
M. A. Lewis and B. Li, Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models, Bull. Math. Biol., 74 (2012), 2383-2402.
doi: 10.1007/s11538-012-9757-6. |
[14] |
J. Mallet-Paret and R. D. Nussbaum, Eigenvalues for a class of homogeneous cone maps arising from max-plus operators, Discr. Cont. Dyn. Sys. (DCDS-A), 8 (2002), 519-562.
doi: 10.3934/dcds.2002.8.519. |
[15] |
J. Mallet-Paret and R. D. Nussbaum, Generalizing the Krein-Rutman theorem, measures of noncompactness and the fixed point index, J. Fixed Point Theory and Appl., 7 (2010), 103-143.
doi: 10.1007/s11784-010-0010-3. |
[16] |
T. E. X. Miller, A. K. Shaw, B. D. Inouye and M. G. Neubert, Sex-biased dispersal and the speed of two-sex invasions, Amer. Nat., 177 (2011), 549-561.
doi: 10.1086/659628. |
[17] |
R. D. Nussbaum, Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem, Fixed Point Theory, (eds. E. Fadell and G. Fournier), Springer, Berlin New York, (1981), 309-331. |
[18] |
R. D. Nussbaum, Eigenvectors of order-preserving linear operators, J. London Math. Soc., 2 (1998), 480-496.
doi: 10.1112/S0024610798006425. |
[19] |
H. H. Schaefer, Halbgeordnete lokalkonvexe Vektorräume. II, Math. Ann., 138 (1959), 259-286.
doi: 10.1007/BF01342907. |
[20] |
H. H. Schaefer, Topological Vector Spaces, Macmillan, New York, 1966. |
[21] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Amer. Math. Soc., Providence, 1995. |
[22] |
H. L. Smith and H. R. Thieme, Dynamical Systems and Population Persistence, AMS, Providence, 2011 |
[23] |
H. R. Thieme, Eigenvectors and eigenfunctionals of homogeneous order-preserving maps, preprint, arXiv:1302.3905. |
[24] |
X.-Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
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