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Stabilization of reaction-diffusion pulses by external forcing.

E P Zemskov1, K Kassner, S C Müller

  • 1Institut für Theoretische Physik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106 Magdeburg, Germany. zemskov@physik.uni-magdeburg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
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This study derives a pulse velocity equation and examines stationary wave conditions. Asymmetric stationary pulses may be stable, unlike symmetric ones, with stability criteria presented.

Area of Science:

  • Nonlinear dynamics
  • Wave propagation physics

Background:

  • Stationary waves and pulse propagation are fundamental in nonlinear systems.
  • Understanding stability conditions is crucial for predicting wave behavior under external forcing.

Purpose of the Study:

  • To derive a pulse velocity equation applicable under forcing conditions.
  • To investigate the conditions for stationary waves, known as pinning conditions.
  • To analyze the stability of different types of stationary pulses.

Main Methods:

  • Derivation of a pulse velocity equation.
  • Analysis of phase-amplitude diagrams to identify stationary pulse types.
  • Application of stability criteria to symmetric and asymmetric parameter sets.

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Main Results:

  • Two distinct types of stationary pulses identified: symmetric and asymmetric parameter sets.
  • Symmetric stationary pulses are found to be universally unstable.
  • Asymmetric stationary pulses exhibit potential for stability, dependent on specific criteria.

Conclusions:

  • The derived pulse velocity equation provides insights into wave dynamics under forcing.
  • Stability is contingent on the asymmetry of the pulse's parameter set.
  • The study presents clear criteria for assessing the stability of stationary pulses.