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...

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Main Authors: Haiyan Gao, Shengmao Fu
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/248657
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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.
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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