A monotone approximation for a size-structured population model with a generalized environment

Journal of Biological Dynamics

Volumn 1, Issue 4, 2007, Pages 305-319

  Ackleh, Azmy S ^a   Deng, Keng ^a   Thibodeaux, Jeremy J ^a  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

Author keywords

Existence uniqueness; Generalized environment; Monotone approximation; Negative growth rates; Numerical simulations; Size structured population model

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ENVIRONMENT; METAMORPHOSIS; PHYSIOLOGY; POPULATION DENSITY; POPULATION DYNAMICS;

ANIMALS; ENVIRONMENT; METAMORPHOSIS, BIOLOGICAL; MODELS, BIOLOGICAL; POPULATION DENSITY; POPULATION DYNAMICS;

EID: 84873706109     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513750701605564     Document Type: Article

References (26)

1. Ackleh, A. S., and Deng, K., 2000. Existence-uniqueness of solutions for a nonlinear nonautonomous size-structured population model:an upper-lower solution approach. Canadian Applied Mathematics Quarterly, 8:1–15.
2. Calsina, A., and El odrissi, O., 2002. Asymptotic behavior of a semilinear age-structured population model with a dynamics for the resource. Mathematical, Computer Modeling, 35:403–427.
3. Calsina, A., and Saldana, J., 1997. Asymptotic behavior of a model of hierarchically structured population dynamics. Journal of Mathematical Biology, 35:967–987.
4. Clemons, C. B., Hariharan, S. I., and Quinn, D. D., 2001. Amplitude equations for time-dependent solutions of the McKendrick equations. SIAM Journal of Applied Mathematics, 62:684–705.
5. Gurtin, M., and MacCamy, R. C., 1974. Nonlinear age-dependent population dynamics. Archive for Rational Mechanics and Analysis, 54:281–300.
6. Kraev, E. A., 2001. Existence and uniqueness for height structured hierarchical population models. Natural Resource Modeling, 14:45–70.
7. Tucker, S. I., and Zimmerman, S. O., 1988. A nonlinear model of population dynamics containing an arbitrary number of continuous structure variables. SIAM Journal of Applied Mathematics, 48:549–591.
8. Lomnicki, A., 1998. Population Ecology of Individuals, Monographs in Population Biology, 25, Princeton:Princeton University Press.
9. Ackleh, A. S., and Deng, K., 2005. Monotone approximation for a hierarchical age-structured population model. Continuous and Discrete Impulse Systems Series B, 12:203–214.
10. Cushing, J., 1994. The dynamics of hierarchical age-structured populations. Journal of Mathematical Biology, 32:705–729.
11. Ackleh, A. S., Deng, K., and Hu, S., 2005. A quasilinear hierarchical size-structured model:well-posedness and approximation. Applied Mathematics and Optimization, 51:35–59.
12. Ackleh, A. S., and Deng, K., 1997. Monotone method for first order nonlocal hyperbolic initial-boundary value problems. Applicable Analysis, 67:283–293.
13. Ackleh, A. S., and Deng, K., 2000. A monotone approximation for a nonlinear nonautonomous size-structured population model. Applied Mathematics and Computation, 108:103–113.
14. Bellman, R., 1973. Methods of Nonlinear Analysis, Vol. II, New York:Academic Press.
15. Ladde, G. S., Lakshmikantham, V., and Vatsala, A. S., 1985. Monotone Iterative Techniques for Nonlinear Differential Equations, Boston:Pitman.
16. Pao, C. V., 1992. Nonlinear Parabolic and Elliptic Equations, New York:Plenum Press.
17. Ackleh, A. S., and Deng, K., 1999. A monotone approxiamtion for the non-autonomous size-structured population model. Quarterly Applied Mathematics, 57:261–267.
18. Abia, L. M., Angulo, O., and López-Marcos, J. C., 2004. Size-structured population dynamics models and their numerical solutions. Discrete and Continuous Dynamical Systems Series Ba, 4:1203–1222.
19. Ackleh, A. S., and Ito, K., 1997. An implicit finite difference scheme for the nonlinear size-structured population Model. Numerical Functional Analysis and Optimization, 18:865–884.
20. Angulo, O., and López-Marcos, J. C., 2004. Numerical integration of fully nonlinear size structured population models. Applied Numerical Mathematics, 50:291–327.
21. Angulo, O., and López-Marcos, J. C., Numerical integration of a size-structured cell population model in an environment of changing substrate concentration. Proceedings of the International Conference on Computational Methods in Sciences and Engineering. Kastoria, Greece. Vol. 1, pp. 28–32.
22. Fairweather, G., and López-Marcos, J. C., 1994. An explicit extrapolated box scheme for the Gurtin–MacCamy equation. Computers & Mathematics with Applications, 27:41–53.
23. Ito, K., Kappel, F., and Peichl, G., 1991. A fully discretized approximation scheme for size-structured population models. SIAM Journal of Numerical Analysis, 28:923–954.
24. Kostova, T., 2003. An explicit third-order numerical method for size-structured population equations. Numerical Methods for Partial Differential Equations, 19:1–21.
25. Sulsky, D., 1993. Numerical solution of structured population models, I, Age structure. Journal of Mathematical Biology, 31:817–839.
26. Sulsky, D., 1994. Numerical solution of structured population models, II, Mass structure. Journal of Mathematical Biology, 32:491–514.