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Convolution Representation of Traveling Pulses in Reaction‐Diffusion Systems

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  • Satoshi Kawaguchi

Abstract

Convolution representation manifests itself as an important tool in the reduction of partial differential equations. In this study, we consider the convolution representation of traveling pulses in reaction‐diffusion systems. Under the adiabatic approximation of inhibitor, a two‐component reaction‐diffusion system is reduced to a one‐component reaction‐diffusion equation with a convolution term. To find the traveling speed in a reaction‐diffusion system with a global coupling term, the stability of the standing pulse and the relation between traveling speed and bifurcation parameter are examined. Additionally, we consider the traveling pulses in the kernel‐based Turing model. The stability of the spatially homogeneous state and most unstable wave number are examined. The practical utilities of the convolution representation of reaction‐diffusion systems are discussed.

Suggested Citation

  • Satoshi Kawaguchi, 2023. "Convolution Representation of Traveling Pulses in Reaction‐Diffusion Systems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:1410642
    DOI: 10.1155/2023/1410642
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    1. Clemens Bachmair & Eckehard Schöll, 2014. "Nonlocal control of pulse propagation in excitable media," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(11), pages 1-10, November.
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