scholarly journals Controlling spatiotemporal chaos in oscillatory reaction–diffusion systems by time-delay autosynchronization

2004 ◽  
Vol 199 (1-2) ◽  
pp. 173-184 ◽  
Author(s):  
C. Beta ◽  
A.S. Mikhailov
Keyword(s):  
Time Delay ◽  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Oscillatory Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

scholarly journals Spatiotemporal chaos and quasipatterns in coupled reaction–diffusion systems

2020 ◽  
Vol 409 ◽  
pp. 132475 ◽  
Author(s):  
Jennifer K. Castelino ◽  
Daniel J. Ratliff ◽  
Alastair M. Rucklidge ◽  
Priya Subramanian ◽  
Chad M. Topaz
Keyword(s):  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Coupled Reaction

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.

Time-delay-induced instabilities in reaction-diffusion systems

2009 ◽  
Vol 80 (4) ◽  
Author(s):  
Shrabani Sen ◽  
Pushpita Ghosh ◽  
Syed Shahed Riaz ◽  
Deb Shankar Ray
Keyword(s):  
Time Delay ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems
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