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Inducing and modulating spiral waves by delayed feedback in a uniform oscillatory reaction–diffusion system

Authors
Journal
Chemical Physics
0301-0104
Publisher
Elsevier
Publication Date
Volume
371
Identifiers
DOI: 10.1016/j.chemphys.2010.04.004
Keywords
  • Reaction–Diffusion System
  • Uniform Oscillation
  • Delayed Feedback
  • Delay-Induced Spiral Waves
  • Dispersion Relation

Abstract

Abstract Spiral waves are induced by delayed feedback in a reaction–diffusion system spontaneously exhibiting a uniform bulk oscillation. Feedback can modulate the spiral wavelength and tip trajectory. For a relatively large feedback intensity ( g > 0.45), the spiral wavelength increases monotonously with an increase in delay time. However, when g < 0.45, the wavelength depends non-monotonously on delay time. Spiral waves are rigid for a moderate delay time, and their tip trajectory radius increases with increasing delay time. When delay time exceeds some critical values, spiral waves begin to meander. The traveling wave dispersion relation of the delayed system is computed to account for the spiral wavelength variation with delay time.

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