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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 908768, 11 pages
On the Multispecies Delayed Gurtin-MacCamy Model
1Faculty of Computer Science, Bialystok University of Technology, Ulica Wiejska 45A, 15-351 Białystok, Poland
2Faculty of Mathematics and Computer Science, Jagiellonian University, Ulica Łojasiewicza 6, 30-348 Kraków, Poland
Received 8 November 2012; Revised 9 March 2013; Accepted 29 March 2013
Academic Editor: Carlos Vazquez
Copyright © 2013 Anna Poskrobko and Antoni Leon Dawidowicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. Hastings, “Interacting age structured populations,” in Mathematical Ecology, vol. 17 of Biomathematics, pp. 287–294, Springer, Berlin, Germany, 1986.
- K. R. Fister and S. Lenhart, “Optimal harvesting in an age-structured predator-prey model,” Applied Mathematics and Optimization, vol. 54, no. 1, pp. 1–15, 2006.
- Z. He and H. Wang, “Control problems of an age-dependent predator-prey system,” Applied Mathematics, vol. 24, no. 3, pp. 253–262, 2009.
- D. S. Levine, “Bifurcating periodic solutions for a class of age-structured predator-prey systems,” Bulletin of Mathematical Biology, vol. 45, no. 6, pp. 901–915, 1983.
- D. J. Wollkind, A. Hastings, and J. A. Logan, “Functional-response, numerical response, and stability in arthropod predator-prey ecosystems involving age structure,” Researches on Population Ecology, vol. 22, pp. 323–338, 1980.
- M. E. Gurtin and R. C. MacCamy, “Non-linear age-dependent population dynamics,” Archive for Rational Mechanics and Analysis, vol. 54, pp. 281–300, 1974.
- D. Breda, M. Iannelli, S. Maset, and R. Vermiglio, “Stability analysis of the Gurtin-MacCamy model,” SIAM Journal on Numerical Analysis, vol. 46, no. 2, pp. 980–995, 2008.
- J. M. Cushing, “The dynamics of hierarchical age-structured populations,” Journal of Mathematical Biology, vol. 32, no. 7, pp. 705–729, 1994.
- A. L. Dawidowicz and A. Poskrobko, “Age-dependent single-species population dynamics with delayed argument,” Mathematical Methods in the Applied Sciences, vol. 33, no. 9, pp. 1122–1135, 2010.
- A. L. Dawidowicz and A. Poskrobko, “On the age-dependent population dynamics with delayed dependence of the structure,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 12, pp. e2657–e2664, 2009.
- G. Di Blasio, “Nonlinear age-dependent population growth with history-dependent birth rate,” Mathematical Biosciences, vol. 46, no. 3-4, pp. 279–291, 1979.
- V. G. Matsenko, “A nonlinear model of the dynamics of the age structure of populations,” Nelīnīĭnī Kolivannya, vol. 6, no. 3, pp. 357–367, 2003.
- S. Piazzera, “An age-dependent population equation with delayed birth process,” Mathematical Methods in the Applied Sciences, vol. 27, no. 4, pp. 427–439, 2004.
- K. E. Swick, “A nonlinear age-dependent model of single species population dynamics,” SIAM Journal on Applied Mathematics, vol. 32, no. 2, pp. 484–498, 1977.
- K. E. Swick, “Periodic solutions of a nonlinear age-dependent model of single species population dynamics,” SIAM Journal on Mathematical Analysis, vol. 11, no. 5, pp. 901–910, 1980.
- Z. G. Bao and W. L. Chan, “A semigroup approach to age-dependent population dynamics with time delay,” Communications in Partial Differential Equations, vol. 14, no. 6, pp. 809–832, 1989.
- O. Arino, E. Sánchez, and G. F. Webb, “Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence,” Journal of Mathematical Analysis and Applications, vol. 215, no. 2, pp. 499–513, 1997.
- O. Arino, E. Sánchez, and G. F. Webb, “Polynomial growth dynamics of telomere loss in a heterogeneous cell population,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 3, no. 3, pp. 263–282, 1997.
- F. Billy, J. Clairambault, O. Fercoq et al., “Synchronisation and control of proliferation in cycling cell population models with age structure,” Mathematics and Computers in Simulation, 2012.
- H. Inaba, “Strong ergodicity for perturbed dual semigroups and application to age-dependent population dynamics,” Journal of Mathematical Analysis and Applications, vol. 165, no. 1, pp. 102–132, 1992.
- I. Roeder, M. Herberg, and M. Horn, “An “age”-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia,” Bulletin of Mathematical Biology, vol. 71, no. 3, pp. 602–626, 2009.
- R. Rundnicki and M. C. Mackey, “Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations,” Journal of Mathematical Analysis and Applications, vol. 187, no. 2, pp. 548–566, 1994.
- J. von Foerster, Some Remarks on Changing Populations, the Kinetics of Cell Proliferation, Grune & Stratton, New York, NY, USA, 1959.