Chaotic behavior of semigroups related to the process of gene amplification-deamplification with cell proliferation.
In the last few years there has been a renewed interest in infinite systems of differential equations, similar to the classical birth-and-death system of population dynamics, due to their rôle in modelling the evolution of drug resistance in cancer cells. In [J. Banasiak, M. Lachowicz, Topological chaos for birth-and-death models with proliferation, Math. Models Methods Appl. Sci. 12 (6) (2002) 755] such systems were shown to generate a chaotic dynamics under, however, very restrictive assumptions on the growth of coefficients. In this paper, using recently developed concept of subspace chaos [J. Banasiak, M. Moszyński, A generalization of Desch-Schappacher-Webb criteria for topological chaos with applications, Discrete Contin. Dyn. Syst. - A 12 (5) (2005) 959], we show that for a linear growth of the coefficients, which are more acceptable from biological point of view, the dynamics of these systems is chaotic in some subspaces of the original state space.
Banasiak
Jacek
J
School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa. banasiak@nu.ac.za
Lachowicz
Mirosław
M
Moszyński
Marcin
M
D000465:Algorithms; D000818:Animals; D002452:Cell Count; D049109:Cell Proliferation; D005784:Gene Amplification; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000235:genetics / Q000473:pathology / Q000503:physiopathology; D017711:Nonlinear Dynamics