Chaos in a fractional-order cancer system

Author

N´Doye, Ibrahima ; Voos, Holger ; Darouach, Mohamed

Author_Institution

Fac. of Sci., Technol. & Commun, Univ. of Luxembourg, Luxembourg, Luxembourg

fYear

2014

fDate

24-27 June 2014

Firstpage

171

Lastpage

176

Abstract

This paper deals with the fractional-order cancer system. It is based on the chaotic system concept, where the mathematical model of system contains fractional-order derivatives. We develop a fractional-order dynamical model of cancer growth, which includes the interactions between healthy tissue cells, tumor cells, and activated immune system cells, clearly leading to chaotic behavior. We perform equilibrium point analysis, indicate the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate order cancer system with total order less than 3, which exhibits chaos, are presented as well.

Keywords

biological tissues; cancer; chaos; differential equations; stability; activated immune system cells; cancer growth; chaotic system; fractional-order cancer system; fractional-order differential equations; fractional-order dynamical model; healthy tissue cells; mathematical model; stability analysis; tumor cells; Cancer; Chaos; Differential equations; Eigenvalues and eigenfunctions; Fractional calculus; Stability analysis; Fractional calculus; chaos; chaotic attractor; fractional-order cancer system; tumor growth;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (ECC), 2014 European

Conference_Location

Strasbourg

Print_ISBN

978-3-9524269-1-3

Type

conf

DOI

10.1109/ECC.2014.6862202

Filename

6862202