https://doi.org/10.1140/epjst/e2014-02254-3
Review
Distribution of chaos and periodic spikes in a three-cell population model of cancer
Auto-organization of oscillatory phases in parameter planes
1 Center for Research & Grants, Baptist Health South Florida, Miami, FL 33143, USA
2 Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Brazil
3 Instituto de Altos Estudos da Paraíba, Rua Infante Dom Henrique 100–1801, 58039-150 João Pessoa, Brazil
4 Institute for Multiscale Simulations, Friedrich-Alexander-Universität, 91052 Erlangen, Germany
5 Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
6 Department of Mathematics, Imperial College London, Huxley Building, 180 Queen's Gate, London SW7 2AZ, UK
Received: 11 April 2014
Revised: 18 August 2014
Published online: 24 October 2014
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.
© EDP Sciences, Springer-Verlag, 2014
