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Stability Analysis and Comparison of the Models for Carcinogenesis Mutations in the Case of Two Stages of Mutations
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U. Foryś
Published/Copyright:
June 9, 2010
Abstract
The present paper is focused on the analysis of three very simple models of carcinogenesis mutations that are based on reaction-diffusion systems and Lotka-Volterra food chains. We consider the case with two stages of mutations and study the systems of three reaction-diffusion equations with zero-flux boundary conditions. We focus on the Turing instability and show that this type of instability is not possible for these models. We also propose some modifications of the considered equations. Results are illustrated by computer simulations.
Key words and phrases.: Carcinogenesis mutation; Bening; pre-malignant and malignant stages of mutations; reaction - diffusion equation; Lotka-Volterra food chain; equilibrium state; stability; global stability; Turing instability
Received: 2004-07-12
Revised: 2004-09-20
Published Online: 2010-06-09
Published in Print: 2005-December
© Heldermann Verlag
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Articles in the same Issue
- On Additive Almost Continuous Functions Under
- Maximal Solutions and Existence Theory for Fuzzy Differential and Integral Equations
- Projections in Weakly Compactly Generated Banach Spaces and Chang's Conjecture
- Dominated Convergence and Stone-Weierstrass Theorem
- Optimality Conditions and Duality for Multiobjective Control Problems
- On the Convergence of Sequences of Functions which are Discontinuous on Countable Sets
- Euler-Poincaré Formalism of Coupled KdV Type Systems and Diffeomorphism Group on S1
- Stability Analysis and Comparison of the Models for Carcinogenesis Mutations in the Case of Two Stages of Mutations
