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December  2013, 18(10): i-ii. doi: 10.3934/dcdsb.2013.18.10i

Preface

Thomas Hillen 1, and  Michael Winkler 2,

1. 

Centre for Mathematical Biology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G2G1
2. 

Institute of Mathematics, University of Paderborn, Warburger Str. 100, 33098 Paderborn

Published  October 2013

Self-organization of micro organisms through the oriented movement of individuals along chemical gradients has caught researchers' imagination and interest for a long time. In fact, the process of aggregation of cells is a first step in the transition from individuals to a collective. Chemotaxis has been identified to play an important role in areas as diverse as ecological species (e.g. slime molds) and bacteria (E. coli), embryogenesis, immune response, wound healing, and cancer development. The first mathematical model for chemotaxis was introduced by Patlak (1953) and became later known as the Keller and Segel (1970) system of equations. The model has become a hot topic not only for the description of biological phenomena, but also mathematically. Sophisticated mathematical analysis has developed and it is the purpose of this special issue of DCDS-B to showcase some of the interesting and challenging mathematical questions that currently arise in the analysis of chemotaxis models.

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Citation: Thomas Hillen, Michael Winkler. Preface. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : i-ii. doi: 10.3934/dcdsb.2013.18.10i
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