Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2015 (2015), Article ID 241312, 7 pages
http://dx.doi.org/10.1155/2015/241312
Research Article

Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey

1CIMAT, Jalisco, s/n, 36240 Col Valenciana, GTO, Mexico
2Universidad Autónoma de Aguascalientes, Edificio 26, Avenida Universidad No. 940, 20100 Aguascalientes, AGS, Mexico

Received 9 September 2014; Revised 15 December 2014; Accepted 16 December 2014

Academic Editor: Wanbiao Ma

Copyright © 2015 Francisco J. Solis and Roberto A. Ku-Carrillo. 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. N. Bairagi and D. Jana, “Age-structured predator-prey model with habitat complexity: oscillations and control,” Dynamical Systems, vol. 27, no. 4, pp. 475–499, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. E. Brooks-Pollock, T. Cohen, and M. Murray, “The impact of realistic age structure in simple models of tuberculosis transmission,” PLoS ONE, vol. 5, no. 1, Article ID e8479, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Ducrot, “Travelling wave solutions for a scalar age-structured equation,” Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, vol. 7, no. 2, pp. 251–273, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  4. W. Feng, M. T. Cowen, and X. Lu, “Coexistence and asymptotic stability in stage-structured predator-prey models,” Mathematical Biosciences and Engineering, vol. 11, no. 4, pp. 823–839, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. M. E. Gurtin, “A system of equations for age dependent population diffusion,” Journal of Theoretical Biology, vol. 40, no. 2, pp. 389–392, 1973. View at Publisher · View at Google Scholar · View at Scopus
  6. M. E. Gurtin and R. C. MacCamy, “Some simple models for nonlinear age-dependent population dynamics,” Mathematical Biosciences, vol. 43, no. 3-4, pp. 199–211, 1979. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. T. K. Kar and S. Jana, “Stability and bifurcation analysis of a stage structured predator prey model with time delay,” Applied Mathematics and Computation, vol. 219, no. 8, pp. 3779–3792, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. D. Levine and M. Gurtin, “Models of predator and cannibalism in age-structured populations,” in Differential Equations and Applications in Ecology, pp. 145–159, 1981. View at Google Scholar
  9. M. Marvá, A. Moussaouí, R. B. de la Parra, and P. Auger, “A density-dependent model describing age-structured population dynamics using hawk-dove tactics,” Journal of Difference Equations and Applications, vol. 19, no. 6, pp. 1022–1034, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. V. Pavlová and L. Berec, “Impacts of predation on dynamics of age-structured prey: allee effects and multi-stability,” Theoretical Ecology, vol. 5, no. 4, pp. 533–544, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. A. McKendrick, Applications of Mathematics to Medical Problems, Springer, 1997.
  12. H. I. Freedman, J. W. So, and J. H. Wu, “A model for the growth of a population exhibiting stage structure: cannibalism and cooperation,” Journal of Computational and Applied Mathematics, vol. 52, no. 1–3, pp. 177–198, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. D. S. Levine, “On the stability of a predator-prey system with egg-eating predators,” Mathematical Biosciences, vol. 56, no. 1-2, pp. 27–46, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  14. H. P. Benoît, E. McCauley, and J. R. Post, “Testing the demographic consequences of cannibalism in Tribolium confusum,” Ecology, vol. 79, no. 8, pp. 2839–2851, 1998. View at Publisher · View at Google Scholar · View at Scopus
  15. P. W. Flinn and J. F. Campbell, “Effects of flour conditioning on cannibalism of T. Castaneum eggs and pupae,” Environmental Entomology, vol. 41, no. 6, pp. 1501–1504, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Fernández, “Cannibalism in dungeness crab Cancer magister: effects of predator-prey size ratio, density, and habitat type,” Marine Ecology Progress Series, vol. 182, pp. 221–230, 1999. View at Publisher · View at Google Scholar · View at Scopus
  17. F. J. Solis and R. A. Ku-Carrillo, “Generic predation in age structure predator-prey models,” Applied Mathematics and Computation, vol. 231, pp. 205–213, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. F. J. Solis, “Self-limitation, fishing and cannibalism,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 39–48, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. F. J. Solis and R. A. Ku, “Nonlinear juvenile predation population dynamics,” Mathematical and Computer Modelling, vol. 54, no. 7-8, pp. 1687–1692, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. D. S. Levine, “Models of age-dependent predation and cannibalism via the McKendrick equation,” Computers and Mathematics with Applications, vol. 9, no. 3, pp. 403–414, 1983. View at Publisher · View at Google Scholar · View at Scopus