Ngwa, G. A. and Maini, P. K. (1995) Spatiotemporal patterns in a mechanical model for mesenchymal morphogenesis. Journal of Mathematical Biology, 33 (5). pp. 489520.

PDF
1MB 
Abstract
We present an indepth study of spatiotemporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system wellposed. We firstly consider onedimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In twodimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two submodels, only one of which is capable of generating pattern. We thus focus on this particular submodel. We present a nonlinear analysis of spatiotemporal patterns exhibited by the submodel on a square domain and discuss mode interaction. Our analysis shows that when a twodimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation.
Item Type:  Article 

Uncontrolled Keywords:  Spatiotemporal  Degenerate modes  Periodic patterns  Hopf bifurcation 
Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Centre for Mathematical Biology 
ID Code:  487 
Deposited By:  Philip Maini 
Deposited On:  10 Dec 2006 
Last Modified:  29 May 2015 18:23 
Repository Staff Only: item control page