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CHAOS IN A THREE-DIMENSIONAL CANCER MODEL

MEHMET ITIK

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

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and

STEPHEN P. BANKS

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

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https://doi.org/10.1142/S0218127410025417Cited by:135 (Source: Crossref)

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.

Keywords:

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