Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2006 (2006), Article ID 60643, 8 pages
http://dx.doi.org/10.1155/JAM/2006/60643

On the linearized stability of age-structured multispecies populations

Department of Mathematical Sciences, The Universityof Memphis, Memphis 38152, TN, USA

Received 3 February 2006; Revised 24 April 2006; Accepted 8 May 2006

Copyright © 2006 Jozsef Z. Farkas. 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.

Linked References

  1. O. Diekmann, M. Gyllenberg, H. Huang, M. Kirkilionis, J. A. J. Metz, and H. R. Thieme, “On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory,” Journal of Mathematical Biology, vol. 43, no. 2, pp. 157–189, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. O. Diekmann, M. Gyllenberg, and J. A. J. Metz, “Physiologically structured population models: toward a general mathematical theory,” preprint.
  3. O. Diekmann, M. Gyllenberg, J. A. J. Metz, and H. R. Thieme, “On the formulation and analysis of general deterministic structured population models. I. Linear theory,” Journal of Mathematical Biology, vol. 36, no. 4, pp. 349–388, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, vol. 194 of Graduate Texts in Mathematics, Springer, New York, 2000. View at Zentralblatt MATH · View at MathSciNet
  5. M. Farkas, “On the stability of stationary age distributions,” Applied Mathematics and Computation, vol. 131, no. 1, pp. 107–123, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. Z. Farkas, “Stability conditions for the non-linear McKendrick equations,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 771–777, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Z. Farkas, “Stability conditions for a non-linear size-structured model,” Nonlinear Analysis. Real World Applications, vol. 6, no. 5, pp. 962–969, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Z. Farkas and T. Hagen, “Stability and regularity results for a size-structured population model,” to appear in Journal of Mathematical Analysis and Applications.
  9. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Giardini Editori, Pisa, 1994.
  11. N. Kato, “A principle of linearized stability for nonlinear evolution equations,” Transactions of the American Mathematical Society, vol. 347, no. 8, pp. 2851–2868, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. A. J. Metz and O. Diekmann, The Dynamics of Physiologically Structured Populations, vol. 68 of Lecture Notes in Biomathematics, Springer, Berlin, 1986. View at Zentralblatt MATH · View at MathSciNet
  13. J. Prüß, “Stability analysis for equilibria in age-specific population dynamics,” Nonlinear Analysis. Theory, Methods & Applications, vol. 7, no. 12, pp. 1291–1313, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. G. F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, vol. 89 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, 1985. View at Zentralblatt MATH · View at MathSciNet