文献类型：期刊文献

英文题名：Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem

作者：Wang, Xuefeng[1];Xu, Qian[2,3]

第一作者：Wang, Xuefeng

通讯作者：Wang, XF[1]

机构：[1]Tulane Univ, Dept Math, New Orleans, LA 70118 USA;[2]Capital Normal Univ, Dept Math, Beijing 100048, Peoples R China;[3]Beijing Union Univ, Basic Courses Dept, Beijing 100101, Peoples R China

第一机构：Tulane Univ, Dept Math, New Orleans, LA 70118 USA

通讯机构：[1]corresponding author), Tulane Univ, Dept Math, New Orleans, LA 70118 USA.

年份：2013

卷号：66

期号：6

起止页码：1241-1266

外文期刊名：JOURNAL OF MATHEMATICAL BIOLOGY

收录：;Scopus(收录号：2-s2.0-84876089117);WOS:【SCI-EXPANDED(收录号:WOS:000317627100005)】；

基金：Part of the work of XFW was carried out when he was visiting Capital Normal University; we wish to thank Professor Yaping Wu and the Mathematics Department for their support. We are also grateful for the helpful comments of the three anonymous referees on the exposition in the paper. This work is also partially supported by NSF DMS-0707796, NNSF of China 11071172 and SRFDF 20101108110001.

语种：英文

摘要：The most important phenomenon in chemotaxis is cell aggregation. To model this phenomenon we use spiky or transition layer (step-function-like) steady states. In the case of one spatial dimension, we carry out global bifurcation analysis on the Keller-Segel model and several variants of it, showing that positive steady states exist if the chemotactic coefficient is larger than a bifurcation value which can be explicitly expressed in terms of the parameters in the models; then we use Helly's compactness theorem to obtain the profiles of these steady states when the ratio of the chemotactic coefficient and the cell diffusion rate is large, showing that they are either spiky or have the transition layer structure. Our results provide insights on how the biological parameters affect pattern formation, and reveal the similarities and differences of some popular chemotaxis models.