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Pulse dynamics in an excitable reaction – diffusion system
Author(s) -
Ohta T.,
Ito T.
Publication year - 2000
Publication title -
macromolecular symposia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.257
H-Index - 76
eISSN - 1521-3900
pISSN - 1022-1360
DOI - 10.1002/1521-3900(200010)160:1<15::aid-masy15>3.0.co;2-0
Subject(s) - bifurcation , pulse (music) , physics , reaction–diffusion system , merge (version control) , classical mechanics , infinitesimal , statistical physics , mathematical analysis , mechanics , mathematics , optics , quantum mechanics , nonlinear system , detector , computer science , information retrieval
We formulate a theory for pulse dynamics in an excitable reaction‐diffusion system not only in one dimension but also in higher dimensions. In the singular limit where the width of pulse boundaries is infinitesimally thin we derive the equation of motion for a pair of interacting pulses. This equation contains the bifurcation that a motionless pulse loses stability and begins to propagate. The theory predicts the following remarkable properties. When the system is far away from the bifurcation threshold, two propagating pulses merge each other upon head‐on collision. However when the system is close to the threshold the pulses behave as if they are elastic objects. These results are consistent with recent computer simulations.