Uniform Convergent Monotone Iterates for Nonlinear Parabolic Reaction-Diffusion Systems

2017 ◽  
pp. 35-48 ◽  
Author(s):  
Igor Boglaev
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Nonlinear Parabolic

Game of Morphogenesis: What Can We Learn from the Pattern-Form Interplay Models?

1998 ◽  
Vol 08 (05) ◽  
pp. 991-1001 ◽  
Author(s):  
A. V. Spirov
Keyword(s):  
Pattern Formation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Surface Geometry ◽  
Parabolic Pdes ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Nonlinear Parabolic Pdes ◽  
Nonlinear Parabolic ◽  
Secondary Bifurcations

We approach the problem of how the information encoded in linear DNA molecule becomes translated into a three-dimensional form from position of Pattern-Form Interplay Models. The characteristic feature of these models is the existence of feedback loops from (bio)chemical pattern formation to modeling embryo form changes. In accordance with the model the system is open and changes in a pattern give rise to changes in form and these changes in form (surface geometry) cause further pattern changes, and so on. Spontaneous pattern formation takes place in the model as primary and secondary bifurcations of nonlinear parabolic PDEs describing reaction-diffusion systems with imposed gradient. We briefly review the main results of previous works and consider the phenomenon of axis tilting as a case of symmetry breaking via secondary bifurcations. The axis tilting bifurcation occurs as a consequence of position-dependency of diffusion coefficients. The explicit demonstration of this phenomenon in Pattern-Form Interplay Models is believed to be new.

scholarly journals Wavelength Selection by Interrupted Coarsening in Reaction-Diffusion Systems

2021 ◽  
Vol 126 (10) ◽  
Author(s):  
Fridtjof Brauns ◽  
Henrik Weyer ◽  
Jacob Halatek ◽  
Junghoon Yoon ◽  
Erwin Frey
Keyword(s):  
Reaction Diffusion ◽  
Wavelength Selection ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

Bifurcations and Synchronization in Networks of Unstable Reaction–Diffusion Systems

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Alain Miranville ◽  
Guillaume Cantin ◽  
M. A. Aziz-Alaoui
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems
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