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Asymptotic analysis of a size-structured cannibalism population model with delayed birth process
1. | Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China |
2. | Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241 |
References:
[1] |
A. S. Ackleh and K. Ito, Measure-valued solutions for a hierarchically size-structured population, J. Diff. Eq., 217 (2005), 431-455.
doi: 10.1016/j.jde.2004.12.013. |
[2] |
M. Boulanouar, The asymptotic behavior of a structured cell population, J. Evol. Eq., 11 (2011), 531-552.
doi: 10.1007/s00028-011-0100-8. |
[3] |
Ph. Clément, H. J. A. M Heijmans, S. Angenent, C. J. van Duijn, and B. de Pagter, One-Parameter Semigroups, North-Holland, Amsterdam, 1987. |
[4] |
J. M. Cushing, A size-structured model for cannibalism, Theoret. Population Biol., 42 (1992), 347-361.
doi: 10.1016/0040-5809(92)90020-T. |
[5] |
G. Di Blasio, Nonlinear age-dependent population growth with history-dependent birth rate, Math. Biosci.,46 (1979), 279-291.
doi: 10.1016/0025-5564(79)90073-7. |
[6] |
O. Diekmann, Ph. Getto and M. Gyllenberg, Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars, SIAM J. Math. Anal., 39 (2007), 1023-1069.
doi: 10.1137/060659211. |
[7] |
O. Diekmann and M. Gyllenberg, Abstract delay equations inspired by population dynamics, Fun. Anal. Evol. Eq., (2007), 187-200.
doi: 10.1007/978-3-7643-7794-6_12. |
[8] |
K. J. Engel, Operator matrices and systems of evolution equations, RIMS Kokyuroku, 966 (1996), 61-80. |
[9] |
K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York, 2000. |
[10] |
L. R. Fox, Cannibalism in natural populations, Annu. Rev. Ecol. Syst., 6 (1975), 87-106.
doi: 10.1146/annurev.es.06.110175.000511. |
[11] |
J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, J. Math. Anal. Appl., 328 (2007), 119-136.
doi: 10.1016/j.jmaa.2006.05.032. |
[12] |
J. Z. Farkas and T. Hagen, Linear stability and positivity results for a generalized size-structured Daphnia model with inflow, Appl. Anal., 86 (2007), 1087-1103.
doi: 10.1080/00036810701545634. |
[13] |
J. Z. Farkas and T. Hagen, Asymptotic behavior of size-structured populations via juvenile-adult interaction, Discr. Cont. Dyn. Syst. B, 9 (2008), 249-266. |
[14] |
J. Z. Farkas and T. Hagen, Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback, Commun. Pure Appl. Anal., 8 (2009), 1825-1839.
doi: 10.3934/cpaa.2009.8.1825. |
[15] |
G. Fragnelli, A. Idrissi and L. Maniar, The asymptotic behavior of a population equation with diffusion and delayed birth process, Discr. Cont. Dyn. Syst. B, 7 (2007), 735-754.
doi: 10.3934/dcdsb.2007.7.735. |
[16] |
X. Fu and D. Zhu, Stability results for a size-structured population model with delayed birth process, Discr. Cont. Dyn. Syst. B, 18 (2013), 109-131.
doi: 10.3934/dcdsb.2013.18.109. |
[17] |
X. Fu and D. Zhu, Stability analysis for a size-structured juvenile-adult population model, Discr. Cont. Dyn. Syst. B, 19 (2014), 391-417.
doi: 10.3934/dcdsb.2014.19.391. |
[18] |
M. Gyllenberg and G. F. Webb, Asynchronous exponential growth of semigroups of nonlinear operators, J. Math. Anal. Appl., 167 (1992), 443-467.
doi: 10.1016/0022-247X(92)90218-3. |
[19] |
Ph. Getto, O. Diekmann, and A. M. de Roos, On the (dis)advantages of cannibalism, J. Math. Biol., 51 (2005), 695-712.
doi: 10.1007/s00285-005-0342-6. |
[20] |
G. Greiner, A typical Perron-Frobenius theorem with applications to an age-dependent populationequation, Lect. Notes in Math., 1076 (1984), 86-100.
doi: 10.1007/BFb0072769. |
[21] |
G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math., 13 (1987), 213-229. |
[22] |
B-Z Guo, W-L Chan, A semigroup approach to age dependent population dynamics with time delay, Comm. PDEs, 14 (1989), 809-832.
doi: 10.1080/03605308908820630. |
[23] |
T. Hagen, Eigenvalue asymptotics in isothermal forced elongation, J. Math. Anal. Appl., 224 (2000), 393-407.
doi: 10.1006/jmaa.1999.6708. |
[24] |
T. Hagen and M. Renardy, Eigenvalue asymptotics in nonisothermal elongational flow, J. Math. Anal. Appl., 252 (2000), 431-443.
doi: 10.1006/jmaa.2000.7089. |
[25] |
A. J. Metz and O. Diekmann, The Dynamics of Psyiologically Structured Populations, Springer, Berlin, 1986. |
[26] |
R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Anal., 89 (1990), 291-302.
doi: 10.1016/0022-1236(90)90096-4. |
[27] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[28] |
S. Pizzera, An age dependent population equation with delayed birth press, Math. Meth. Appl. Sci., 27 (2004), 427-439.
doi: 10.1002/mma.462. |
[29] |
S. Pizzera and L. Tonetto, Asynchronous exponential growth for an age dependent population equation with delayed birth process, J. Evol. Equ., 5 (2005), 61-77.
doi: 10.1007/s00028-004-0159-6. |
[30] |
K. E. Swick, A nonlinear age-dependent model of single species population dynamics, SIAM J. Appl. Math., 32 (1977), 484-498.
doi: 10.1137/0132040. |
[31] |
K. E. Swick, Periodic solutions of a nonlinear age-dependent model of single species population dynamics, SIAM J. Math. Anal., 11 (1980), 901-910.
doi: 10.1137/0511080. |
[32] |
G. F. Webb, Theory of Nonlinear Age-dependent Population Dynamics, Marcell Dekker, New York, 1985. |
show all references
References:
[1] |
A. S. Ackleh and K. Ito, Measure-valued solutions for a hierarchically size-structured population, J. Diff. Eq., 217 (2005), 431-455.
doi: 10.1016/j.jde.2004.12.013. |
[2] |
M. Boulanouar, The asymptotic behavior of a structured cell population, J. Evol. Eq., 11 (2011), 531-552.
doi: 10.1007/s00028-011-0100-8. |
[3] |
Ph. Clément, H. J. A. M Heijmans, S. Angenent, C. J. van Duijn, and B. de Pagter, One-Parameter Semigroups, North-Holland, Amsterdam, 1987. |
[4] |
J. M. Cushing, A size-structured model for cannibalism, Theoret. Population Biol., 42 (1992), 347-361.
doi: 10.1016/0040-5809(92)90020-T. |
[5] |
G. Di Blasio, Nonlinear age-dependent population growth with history-dependent birth rate, Math. Biosci.,46 (1979), 279-291.
doi: 10.1016/0025-5564(79)90073-7. |
[6] |
O. Diekmann, Ph. Getto and M. Gyllenberg, Stability and bifurcation analysis of Volterra functional equations in the light of suns and stars, SIAM J. Math. Anal., 39 (2007), 1023-1069.
doi: 10.1137/060659211. |
[7] |
O. Diekmann and M. Gyllenberg, Abstract delay equations inspired by population dynamics, Fun. Anal. Evol. Eq., (2007), 187-200.
doi: 10.1007/978-3-7643-7794-6_12. |
[8] |
K. J. Engel, Operator matrices and systems of evolution equations, RIMS Kokyuroku, 966 (1996), 61-80. |
[9] |
K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York, 2000. |
[10] |
L. R. Fox, Cannibalism in natural populations, Annu. Rev. Ecol. Syst., 6 (1975), 87-106.
doi: 10.1146/annurev.es.06.110175.000511. |
[11] |
J. Z. Farkas and T. Hagen, Stability and regularity results for a size-structured population model, J. Math. Anal. Appl., 328 (2007), 119-136.
doi: 10.1016/j.jmaa.2006.05.032. |
[12] |
J. Z. Farkas and T. Hagen, Linear stability and positivity results for a generalized size-structured Daphnia model with inflow, Appl. Anal., 86 (2007), 1087-1103.
doi: 10.1080/00036810701545634. |
[13] |
J. Z. Farkas and T. Hagen, Asymptotic behavior of size-structured populations via juvenile-adult interaction, Discr. Cont. Dyn. Syst. B, 9 (2008), 249-266. |
[14] |
J. Z. Farkas and T. Hagen, Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback, Commun. Pure Appl. Anal., 8 (2009), 1825-1839.
doi: 10.3934/cpaa.2009.8.1825. |
[15] |
G. Fragnelli, A. Idrissi and L. Maniar, The asymptotic behavior of a population equation with diffusion and delayed birth process, Discr. Cont. Dyn. Syst. B, 7 (2007), 735-754.
doi: 10.3934/dcdsb.2007.7.735. |
[16] |
X. Fu and D. Zhu, Stability results for a size-structured population model with delayed birth process, Discr. Cont. Dyn. Syst. B, 18 (2013), 109-131.
doi: 10.3934/dcdsb.2013.18.109. |
[17] |
X. Fu and D. Zhu, Stability analysis for a size-structured juvenile-adult population model, Discr. Cont. Dyn. Syst. B, 19 (2014), 391-417.
doi: 10.3934/dcdsb.2014.19.391. |
[18] |
M. Gyllenberg and G. F. Webb, Asynchronous exponential growth of semigroups of nonlinear operators, J. Math. Anal. Appl., 167 (1992), 443-467.
doi: 10.1016/0022-247X(92)90218-3. |
[19] |
Ph. Getto, O. Diekmann, and A. M. de Roos, On the (dis)advantages of cannibalism, J. Math. Biol., 51 (2005), 695-712.
doi: 10.1007/s00285-005-0342-6. |
[20] |
G. Greiner, A typical Perron-Frobenius theorem with applications to an age-dependent populationequation, Lect. Notes in Math., 1076 (1984), 86-100.
doi: 10.1007/BFb0072769. |
[21] |
G. Greiner, Perturbing the boundary conditions of a generator, Houston J. Math., 13 (1987), 213-229. |
[22] |
B-Z Guo, W-L Chan, A semigroup approach to age dependent population dynamics with time delay, Comm. PDEs, 14 (1989), 809-832.
doi: 10.1080/03605308908820630. |
[23] |
T. Hagen, Eigenvalue asymptotics in isothermal forced elongation, J. Math. Anal. Appl., 224 (2000), 393-407.
doi: 10.1006/jmaa.1999.6708. |
[24] |
T. Hagen and M. Renardy, Eigenvalue asymptotics in nonisothermal elongational flow, J. Math. Anal. Appl., 252 (2000), 431-443.
doi: 10.1006/jmaa.2000.7089. |
[25] |
A. J. Metz and O. Diekmann, The Dynamics of Psyiologically Structured Populations, Springer, Berlin, 1986. |
[26] |
R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Anal., 89 (1990), 291-302.
doi: 10.1016/0022-1236(90)90096-4. |
[27] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[28] |
S. Pizzera, An age dependent population equation with delayed birth press, Math. Meth. Appl. Sci., 27 (2004), 427-439.
doi: 10.1002/mma.462. |
[29] |
S. Pizzera and L. Tonetto, Asynchronous exponential growth for an age dependent population equation with delayed birth process, J. Evol. Equ., 5 (2005), 61-77.
doi: 10.1007/s00028-004-0159-6. |
[30] |
K. E. Swick, A nonlinear age-dependent model of single species population dynamics, SIAM J. Appl. Math., 32 (1977), 484-498.
doi: 10.1137/0132040. |
[31] |
K. E. Swick, Periodic solutions of a nonlinear age-dependent model of single species population dynamics, SIAM J. Math. Anal., 11 (1980), 901-910.
doi: 10.1137/0511080. |
[32] |
G. F. Webb, Theory of Nonlinear Age-dependent Population Dynamics, Marcell Dekker, New York, 1985. |
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