scholarly journals Phase plane analysis of travelling waves for higher order autocatalytic reaction-diffusion systems

2007 ◽  
Vol 8 (1) ◽  
pp. 115-125 ◽  
Author(s):  
Yuzo Hosono ◽  
Keyword(s):  
Phase Plane ◽  
Travelling Waves ◽  
Reaction Diffusion ◽  
Higher Order ◽  
Autocatalytic Reaction ◽  
Phase Plane Analysis ◽  
Reaction Diffusion Systems ◽  
Plane Analysis ◽  
Diffusion Systems

Noise-induced suppression of periodic travelling waves in oscillatory reaction–diffusion systems

2010 ◽  
Vol 466 (2119) ◽  
pp. 1903-1917 ◽  
Author(s):  
Michael Sieber ◽  
Horst Malchow ◽  
Sergei V. Petrovskii
Keyword(s):  
Travelling Waves ◽  
Natural Populations ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Oscillatory Reaction ◽  
Stochastic Forcing ◽  
Spatial Direction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Spatio Temporal

Ecological field data suggest that some species show periodic changes in abundance over time and in a specific spatial direction. Periodic travelling waves as solutions to reaction–diffusion equations have helped to identify possible scenarios, by which such spatio-temporal patterns may arise. In this paper, such solutions are tested for their robustness against an irregular temporal forcing, since most natural populations can be expected to be subject to erratic fluctuations imposed by the environment. It is found that small environmental noise is able to suppress periodic travelling waves in stochastic variants of oscillatory reaction–diffusion systems. Irregular spatio-temporal oscillations, however, appear to be more robust and persist under the same stochastic forcing.

Computational Study of Traveling Wave Solutions of Isothermal Chemical Systems

2016 ◽  
Vol 19 (5) ◽  
pp. 1461-1472 ◽  
Author(s):  
Yuanwei Qi ◽  
Yi Zhu
Keyword(s):  
Chemical Reaction ◽  
Traveling Waves ◽  
Flow Reactor ◽  
Computational Study ◽  
Chemical Species ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Autocatalytic Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

AbstractThis article studies propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will be studied. The first is autocatalytic chemical reaction of order m without decay. The second is chemical reaction of order m with a decay of order n, where m and n are positive integers and m>n≥1. A typical system in autocatalysis is A+2B→3B and B→C involving two chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.The numerical computation gives more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves.For autocatalytic reaction of order m = 2 with linear decay n = 1, which has a particular important role in chemical waves, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.

Instability and pattern formation in reaction-diffusion systems: A higher order analysis

2007 ◽  
Vol 127 (6) ◽  
pp. 064503 ◽  
Author(s):  
Syed Shahed Riaz ◽  
Rahul Sharma ◽  
S. P. Bhattacharyya ◽  
D. S. Ray
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Higher Order ◽  
Reaction Diffusion Systems ◽  
Order Analysis ◽  
Diffusion Systems
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