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Spatiotemporal antiresonance in coupled reaction-diffusion systems.

Krishnendu Pal1, Shibashis Paul1, Deb Shankar Ray1

  • 1Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.

Physical Review. E
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Summary

This study explores spatiotemporal antiresonance in coupled chemical reactions. We found destructive interference between coupling and forcing creates unique pattern emergence in undriven systems.

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Area of Science:

  • Chemical kinetics
  • Nonlinear dynamics
  • Reaction-diffusion systems

Background:

  • Antiresonance is a known physical phenomenon, but its study in coupled chemical reactions is limited.
  • Reaction-diffusion systems are crucial for understanding pattern formation in chemical and biological systems.

Purpose of the Study:

  • To theoretically investigate spatiotemporal antiresonance in diffusively coupled chemical reactions.
  • To analyze the influence of external periodic forcing on the antiresonance phenomenon.
  • To derive analytical expressions for amplitude-frequency response functions.

Main Methods:

  • Linearized dynamics around the steady state of two-component coupled reaction-diffusion systems.
  • Derivation of general analytical expressions for amplitude-frequency response functions.
  • Numerical simulations using coupled Gray-Scott reaction-diffusion systems.

Main Results:

  • Antiresonance dips were observed in the amplitude-frequency response curves.
  • Destructive interference between system coupling and external forcing was identified as the cause.
  • Differential stability of subsystems led to pattern emergence in the undriven component.

Conclusions:

  • The study provides a theoretical framework for understanding antiresonance in coupled chemical systems.
  • External forcing can induce complex spatiotemporal patterns via antiresonance.
  • The findings highlight the interplay between coupling, forcing, and stability in reaction-diffusion systems.