CHAOS IN A THREE-DIMENSIONAL CANCER MODEL


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Itik M. , Banks S. P.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, vol.20, no.1, pp.71-79, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.1142/s0218127410025417
  • Title of Journal : INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
  • Page Numbers: pp.71-79

Abstract

In this study, we develop a new dynamical model of cancer growth, which includes the interactions between tumour cells, healthy tissue cells, and activated immune system cells, clearly leading to chaotic behavior. We explain the biological relevance of our model and the ways in which it differs from the existing ones. We perform equilibria analysis, indicate the conditions where chaotic dynamics can be observed, and show rigorously the existence of chaos by calculating the Lyapunov exponents and the Lyapunov dimension of the system. Moreover, we demonstrate that Shilnikov's theorem is valid in the parameter range of interest.