Non-linear Diusion for Chemotaxis and Birth-Death Process for Keller-Segel Model

This paper seeks to establish the stability of the birth-death process in relation to the Keller-Segel Model. As well, it attempts to describe the stability of non-linear diusion for chemotaxis. Attention will be on mass criticality results applying to the chemotaxis model. Afterwards, the analysis of the relative stability that stationary states exhibit is undertaken using the Keller-Segel system for the chemotaxis having linear diusion. Standard linearization and separation of variables are the techniques employed in the analysis. The stability or instability of the analysed cases is demonstrated by the graphics. By using the crit- ical results obtained for the models, the graphics are then compared with the rest.