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Updated: Jun 18, 2026

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Radially evolving spiral wave patterns in the Gierer-Meinhardt reaction-diffusion system.

Tarpan Maiti1, Achal Jadhav1, Pushpita Ghosh1

  • 1School of Chemistry, IISER Thiruvananthapuram Kerala 695551 India pushpita@iisertvm.ac.in.

RSC Advances
|March 4, 2025
PubMed
Summary
This summary is machine-generated.

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This study reveals how spiral waves form in reaction-diffusion systems, specifically the Gierer-Meinhardt model. The research shows these spiral waves have an amplitude that changes with radial distance.

Area of Science:

  • * Physical Chemistry
  • * Theoretical Chemistry
  • * Chemical Kinetics

Background:

  • * Spiral wave formation is a key phenomenon in spatially extended reaction-diffusion systems.
  • * These patterns are observed in various natural and chemical processes.
  • * Understanding their emergence is crucial for various scientific disciplines.

Purpose of the Study:

  • * To investigate spiral wave formation in the Gierer-Meinhardt reaction-diffusion model.
  • * To theoretically derive conditions for spiral wave emergence using perturbation techniques.
  • * To analyze the radial dependence of spiral wave amplitude.

Main Methods:

  • * Application of a multiple-time scale perturbation technique.
  • * Derivation of amplitude equations governing spiral wave behavior.

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  • * Numerical simulations to validate theoretical predictions.

    • Main Results:

    • * Identified conditions for the emergence of spiral wave-like patterns.
    • * Demonstrated that spiral wave amplitude varies with radial distance.
    • * Confirmed theoretical findings through numerical simulations.

    Conclusions:

    • * The Gierer-Meinhardt model supports spiral wave formation.
    • * A unique radial amplitude dependence characterizes these spiral waves.
    • * The study provides a theoretical and numerical framework for understanding complex pattern formation.