Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2015 (2015), Article ID 354918, 11 pages
http://dx.doi.org/10.1155/2015/354918
Research Article

Hopf Bifurcation, Cascade of Period-Doubling, Chaos, and the Possibility of Cure in a 3D Cancer Model

Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista (UNESP), 19060-900 Presidente Prudente, SP, Brazil

Received 27 June 2014; Accepted 13 October 2014

Academic Editor: Yongli Song

Copyright © 2015 Marluci Cristina Galindo et al. 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. R. P. Araujo and D. L. McElwain, “A history of the study of solid tumour growth: the contribution of mathematical modelling,” Bulletin of Mathematical Biology, vol. 66, no. 5, pp. 1039–1091, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. R. Chammas, D. Silva, A. Wainstein, and K. Abdallah, “Imunologia clinica das neoplasias,” in Imunologia Clínica na Prática Médica, pp. 447–460, Atheneu, São Paulo, Brazil, 2009. View at Google Scholar
  3. W. Chang, L. Crowl, E. Malm, K. Todd-Brown, L. Thomas, and M. Vrable, Analyzing Immunotherapy and Chemotherapy of Tumors Through Mathematical Modeling, Department of Mathematics, Harvey-Mudd University, Claremont, Calif, USA, 2003.
  4. D. Kirschner and J. C. Panetta, “Modeling immunotherapy of the tumor—immune interaction,” Journal of Mathematical Biology, vol. 37, no. 3, pp. 235–252, 1998. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Galach, “Dynamics of the tumor-immune system competition—the effect of time delay,” International Journal of Applied Mathematics and Computer Science, vol. 13, no. 3, pp. 395–406, 2003. View at Google Scholar · View at MathSciNet
  6. M. Itik and S. P. Banks, “Chaos in a three-dimensional cancer model,” International Journal of Bifurcation and Chaos, vol. 20, no. 1, pp. 71–79, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. L. G. de Pillis and A. Radunskaya, “The dynamics of an optimally controlled tumor model: a case study,” Mathematical and Computer Modelling, vol. 37, no. 11, pp. 1221–1244, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, New York, NY, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Itik and S. P. Banks, “On the structure of periodic orbits on a simple branched manifold,” International Journal of Bifurcation and Chaos, vol. 20, no. 11, pp. 3517–3528, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. L. S. Pontryagin, Ordinary Differential Equations, Addison-Wesley, New York, NY, USA, 1962. View at MathSciNet
  11. C. Letellier, F. Denis, and L. A. Aguirre, “What can be learned from a chaotic cancer model?” Journal of Theoretical Biology, vol. 322, pp. 7–16, 2013. View at Publisher · View at Google Scholar · View at Scopus