Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth
This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a d-dimensional box Td=(0,π)d (d=1,2,3). It is proved that given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics al...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/248657 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849695511362142208 |
|---|---|
| author | Haiyan Gao Shengmao Fu |
| author_facet | Haiyan Gao Shengmao Fu |
| author_sort | Haiyan Gao |
| collection | DOAJ |
| description | This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a d-dimensional box Td=(0,π)d (d=1,2,3). It is proved that given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order ln(1/δ). Each initial perturbation certainly can behave drastically different from another, which gives rise to the richness of patterns. |
| format | Article |
| id | doaj-art-cfb0fa50fcdd44d2a966b9e2110edf1c |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cfb0fa50fcdd44d2a966b9e2110edf1c2025-08-20T03:19:46ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/248657248657Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic GrowthHaiyan Gao0Shengmao Fu1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaSchool of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, ChinaThis paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a d-dimensional box Td=(0,π)d (d=1,2,3). It is proved that given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order ln(1/δ). Each initial perturbation certainly can behave drastically different from another, which gives rise to the richness of patterns.http://dx.doi.org/10.1155/2014/248657 |
| spellingShingle | Haiyan Gao Shengmao Fu Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth Abstract and Applied Analysis |
| title | Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth |
| title_full | Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth |
| title_fullStr | Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth |
| title_full_unstemmed | Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth |
| title_short | Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth |
| title_sort | nonlinear instability for a volume filling chemotaxis model with logistic growth |
| url | http://dx.doi.org/10.1155/2014/248657 |
| work_keys_str_mv | AT haiyangao nonlinearinstabilityforavolumefillingchemotaxismodelwithlogisticgrowth AT shengmaofu nonlinearinstabilityforavolumefillingchemotaxismodelwithlogisticgrowth |