scholarly journals Chemotaxis-driven pattern formation for a reaction–diffusion–chemotaxis model with volume-filling effect

2016 ◽  
Vol 72 (5) ◽  
pp. 1320-1340 ◽  
Author(s):  
Manjun Ma ◽  
Meiyan Gao ◽  
Changqing Tong ◽  
Yazhou Han
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Chemotaxis Model ◽  
Volume Filling

scholarly journals Pattern formation for a volume-filling chemotaxis model with logistic growth

2017 ◽  
Vol 448 (2) ◽  
pp. 885-907 ◽  
Author(s):  
Yazhou Han ◽  
Zhongfang Li ◽  
Jicheng Tao ◽  
Manjun Ma
Keyword(s):  
Pattern Formation ◽  
Logistic Growth ◽  
Chemotaxis Model ◽  
Volume Filling

Traveling wavefronts for a reaction-diffusion-chemotaxis model with volume-filling effect

2017 ◽  
Vol 32 (1) ◽  
pp. 108-116
Author(s):  
Man-jun Ma ◽  
Hui Li ◽  
Mei-yan Gao ◽  
Ji-cheng Tao ◽  
Ya-zhou Han
Keyword(s):  
Reaction Diffusion ◽  
Chemotaxis Model ◽  
Volume Filling

PATTERN FORMATION IN CHEMOTAXIC REACTION-DIFFUSION SYSTEMS

2012 ◽  
Vol 05 (03) ◽  
pp. 1260013
Author(s):  
HIROTO SHOJI ◽  
KEITARO SAITOH
Keyword(s):  
Free Energy ◽  
Pattern Formation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Volume Filling ◽  
Reaction Diffusion Systems ◽  
Receptor Aggregation ◽  
Diffusion Systems

In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller–Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equilibrium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.

scholarly journals Chemotaxis Model for Drug Delivery Using Turing’s Instability and Non-Linear Diffusion

2021 ◽  
Vol 11 (11) ◽  
pp. 4979
Author(s):  
Mohammed Almijalli ◽  
Moustafa Ibrahim ◽  
Ali Saad ◽  
Mazen Saad
Keyword(s):  
Drug Delivery ◽  
Pattern Formation ◽  
Targeted Drug Delivery ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Orthogonality Condition ◽  
Finite Volume Scheme ◽  
Chemotaxis Model ◽  
Linear Diffusion ◽  
Targeted Drug

This paper is devoted to the study of the chemotaxis model for drug delivery purposes. The pattern formation for a volume-filling with nonlinear diffusive terms is investigated. The proposed mathematical model is governed by a reaction–diffusion system modeling the interaction between the cell density and the concentration of the chemoattractant. We investigate the pattern formation for the model using Turing’s principle and linear stability analysis. An asymptotic expansion is used to linearize the nonlinear diffusive terms. Next, we introduce an implicit finite volume scheme; it is presented on a triangular mesh satisfying the orthogonality condition. Finally, numerical results showing the formation of the spatial pattern for the chemotaxis model are presented and analyzed. The results demonstrate promising progress in understanding the process of controlling and designing targeted drug delivery.

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