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Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth

Part of: Applications - Dynamical systems and ergodic theory Stability theory Mathematical biology in general

Published online by Cambridge University Press:  11 July 2017

P. M. Tchepmo Djomegni  and
K. S. Govinder
P. M. Tchepmo Djomegni*
Affiliation:
School of Mathematics, Statistics and Computer science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa
K. S. Govinder
Affiliation:
School of Mathematics, Statistics and Computer science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa
*
*Corresponding author. Email:ptchepmo@ymail.com, ptchepmo@gmail.com (P. M. T. Djomegni)
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Abstract

Mass migration of cells (via wave motion) plays an important role in many biological processes, particularly chemotaxis. We study the existence of travelling wave solutions for a chemotaxis model on a microscopic scale. The interaction between nutrients and chemoattractants are considered. Unlike previous approaches, we allow for diffusion of substrates, degradation of chemoattractants and cell growth (constant and linear growth rate). We apply asymptotic methods to investigate the behaviour of the solutions when cells are highly sensitive to extracellular signalling. Explicit solutions are demonstrated, and their biological implications are presented. The results presented here extend and generalize known results.

Keywords

Lie symmetriesvelocity-jump processtravelling wavesasymptotic methods

MSC classification

Secondary: 34D20: Stability 37N25: Dynamical systems in biology 92B05: General biology and biomathematics
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1250 - 1270
Copyright
Copyright © Global-Science Press 2017 

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