Geodesic
Destabilization of Localized Structures in Reaction-Diffusion Systems Induced by Delayed Feedback
Svetlana V. Gurevich1 ; Rudolf Friedrich1
1 Institut for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
ESAIM. Proceedings, Tome 39 (2013), pp. 49-56.

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We are interested in the stability of two-dimensional localized structures in reaction-diffusion systems subjected to a delayed feedback. We show that the presence of the delay can induce complex behavior of the localized structures, including, e.g., spontaneous motion or breathing of the localized objects. In the case of spontaneous motion, the corresponding order parameter equation for the position of the localized structure is derived. In addition, numerical simulations are carried out showing good agreement with the analytical predictions.
DOI : 10.1051/proc/201339007

Svetlana V. Gurevich 1 ; Rudolf Friedrich 1

1 Institut for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany 
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     author = {Svetlana V. Gurevich and Rudolf Friedrich},
     title = {Destabilization of {Localized} {Structures} in {Reaction-Diffusion} {Systems} {Induced} by {Delayed} {Feedback}},
     journal = {ESAIM. Proceedings},
     pages = {49--56},
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Svetlana V. Gurevich; Rudolf Friedrich. Destabilization of Localized Structures in Reaction-Diffusion Systems Induced by Delayed Feedback. ESAIM. Proceedings, Tome 39 (2013), pp. 49-56. doi : 10.1051/proc/201339007. http://geodesic.mathdoc.fr/articles/10.1051/proc/201339007/

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