This is the abstract of the paper
  "TOPOLOGICAL CHAOS FOR BIRTH--AND--DEATH--TYPE MODELS  WITH PROLIFERATION}"
by Jacek Banasiak and Miroslaw Lachowicz .

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Abstract:
In this paper we consider a class of infinite systems of linear ODEs.
Each system corresponds to a process characterized by two components: the
conservative one (birth--and--death process) and the proliferative one.
The system of this type can describe the population of neoplastic cells divided
into subpopulations characterized by different levels of cellular resistance to
antineoplastic drugs. Under suitable assumptions on the ``birth'' (amplification)
coefficients, the ``death'' (deamplification) coefficients and the averages of
the life-spans we prove that this class of models is topologically chaotic.

Key words - topological chaos, birth--and--death process, hypercyclic operators,
kinetic model, cancer cells.

 AMS Subject Classification 34G10, 47D06, 47N60, 95C50, 92D25

Jacek Banasiak,
School of Mathematical and Statistical Sciences, University of Natal,
Durban 4041 S$

Miroslaw Lachowicz,
Institute of Applied Mathematics and Mechanics, Warsaw University, ul.
Banacha 2, P$

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