Reaction-Diffusion Systems Arising in Biological and Chemical Systems: Application of Singular Limit Procedures

2003 ◽  
pp. 89-121 ◽  
Author(s):  
Masayasu Mimura
Keyword(s):  
Reaction Diffusion ◽  
Singular Limit ◽  
Reaction Diffusion Systems ◽  
Chemical Systems ◽  
Diffusion Systems

Coupled and forced patterns in reaction–diffusion systems

2007 ◽  
Vol 366 (1864) ◽  
pp. 397-408 ◽  
Author(s):  
Irving R Epstein ◽  
Igal B Berenstein ◽  
Milos Dolnik ◽  
Vladimir K Vanag ◽  
Lingfa Yang ◽  
...  
Keyword(s):  
Plane Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Chemical Systems ◽  
Diffusion Systems ◽  
Spatially Distributed ◽  
Acid Reaction ◽  
Observed Behaviour ◽  
Spatio Temporal ◽  
Turing Structures

Several reaction–diffusion systems that exhibit temporal periodicity when well mixed also display spatio-temporal pattern formation in a spatially distributed, unstirred configuration. These patterns can be travelling (e.g. spirals, concentric circles, plane waves) or stationary in space (Turing structures, standing waves). The behaviour of coupled and forced temporal oscillators has been well studied, but much less is known about the phenomenology of forced and coupled patterns. We present experimental results focusing primarily on coupled patterns in two chemical systems, the chlorine dioxide–iodine–malonic acid reaction and the Belousov–Zhabotinsky reaction. The observed behaviour can be simulated with simple chemically plausible models.

scholarly journals Complex Pacemakers and Wave Sinks in Heterogeneous Oscillatory Chemical Systems

2002 ◽  
Vol 216 (4) ◽  
Author(s):  
Michael Stich ◽  
Alexander S. Mikhailov
Keyword(s):  
Reaction Diffusion ◽  
Frequency Shifts ◽  
Reaction Diffusion Systems ◽  
Sources And Sinks ◽  
Chemical Systems ◽  
Diffusion Systems ◽  
Wave Patterns ◽  
Oscillatory Chemical ◽  
Local Shift ◽  
Phase Slips

We investigate pattern formation in oscillatory reaction-diffusion systems where wave sources and sinks are created by a local shift of the oscillation frequency. General properties of resulting wave patterns in media with positive and negative dispersion are discussed. It is shown that phase slips in the wave patterns develop for strong frequency shifts, indicating the onset of desynchronization in the medium.

scholarly journals Traveling spots and traveling fingers in singular limit problems of reaction-diffusion systems

2014 ◽  
Vol 19 (3) ◽  
pp. 697-714 ◽  
Author(s):  
Yan-Yu Chen ◽  
◽  
Yoshihito Kohsaka ◽  
Hirokazu Ninomiya ◽  
◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Singular Limit ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Limit Problems

scholarly journals Insights from chemical systems into Turing-type morphogenesis

2021 ◽  
Vol 379 (2213) ◽  
Author(s):  
C. Konow ◽  
M. Dolnik ◽  
I. R. Epstein
Keyword(s):  
Reaction Diffusion ◽  
Behavioural Science ◽  
Future Directions ◽  
Reaction Diffusion Systems ◽  
Chemical Systems ◽  
Alan Turing ◽  
Diffusion Systems ◽  
Chemical Studies ◽  
Historical Role ◽  
Turing Mechanism

In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction–diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237 , 37–72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction–diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

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