反应扩散系统中行波脉冲的卷积表示

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2023-03-30 DOI:10.1155/2023/1410642

S. Kawaguchi

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引用次数: 0

摘要

卷积表示是偏微分方程归约的一个重要工具。在这项研究中，我们考虑了反应扩散系统中行进脉冲的卷积表示。在抑制剂的绝热近似下，将双组分反应扩散系统简化为具有卷积项的单组分反应-扩散方程。为了求出具有全局耦合项的反应扩散系统的行进速度，研究了驻波的稳定性以及行进速度与分岔参数之间的关系。此外，我们还考虑了基于核的图灵模型中的行波脉冲。研究了空间均匀态的稳定性和最不稳定波数。讨论了反应扩散系统卷积表示的实用性。

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Convolution Representation of Traveling Pulses in Reaction-Diffusion Systems

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.

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来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.