The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2131–2144 | Cite as

Distribution of chaos and periodic spikes in a three-cell population model of cancer

Auto-organization of oscillatory phases in parameter planes
  • Michelle R. Gallas
  • Marcia R. Gallas
  • Jason A.C. Gallas
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications


We study complex oscillations generated by the de Pillis-Radunskaya model of cancer growth, a model including interactions between tumor cells, healthy cells, and activated immune system cells. We report a wide-ranging systematic numerical classification of the oscillatory states and of their relative abundance. The dynamical states of the cell populations are characterized here by two independent and complementary types of stability diagrams: Lyapunov and isospike diagrams. The model is found to display stability phases organized regularly in old and new ways: Apart from the familiar spirals of stability, it displays exceptionally long zig-zag networks and intermixed cascades of two- and three-doubling flanked stability islands previously detected only in feedback systems with delay. In addition, we also characterize the interplay between continuous spike-adding and spike-doubling mechanisms responsible for the unbounded complexification of periodic wave patterns. This article is dedicated to Prof. Hans Jürgen Herrmann on the occasion of his 60th birthday.


Lyapunov Exponent European Physical Journal Special Topic Cancer Model Stability Diagram Control Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  • Michelle R. Gallas
    • 1
  • Marcia R. Gallas
    • 2
    • 3
    • 4
    • 5
    • 6
  • Jason A.C. Gallas
    • 2
    • 3
    • 4
    • 5
    • 6
  1. 1.Center for Research & Grants, Baptist Health South FloridaMiamiUSA
  2. 2.Departamento de Física, Universidade Federal da ParaíbaJoão PessoaBrazil
  3. 3.Instituto de Altos Estudos da ParaíbaJoão PessoaBrazil
  4. 4.Institute for Multiscale Simulations, Friedrich-Alexander-UniversitätErlangenGermany
  5. 5.Max-Planck-Institute for the Physics of Complex SystemsDresdenGermany
  6. 6.Department of MathematicsImperial College LondonLondonUK

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