Isolated periodic wave trains in a generalized Burgers–Huxley equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.14232/ejqtde.2022.1.4

Qinlong Wang, Yu'e Xiong, Wentao Huang, V. Romanovski

引用次数: 1

Abstract

We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with a degenerate equilibrium arising after the traveling transformation are investigated. By finding certain positive definite Lyapunov functions in the neighborhood of the degenerate singular points and the Hopf bifurcation points, the number of possible limit cycles in the corresponding planar systems is determined. The existence of isolated periodic wave trains in the equation is established, which is universal for any positive integer n in this model. Within the process, one interesting example is obtained, namely a series of limit cycles bifurcating from a semi-hyperbolic singular point with one zero eigenvalue and one non-zero eigenvalue for its Jacobi matrix.

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广义Burgers-Huxley方程中的孤立周期波列

研究了一类修正广义Burgers-Huxley方程中的孤立周期波列。研究了行变换后产生的平面简并平衡系统。通过在退化奇点和Hopf分岔点的邻域中寻找某些正定Lyapunov函数，确定了相应平面系统中可能存在的极限环数。建立了方程中孤立周期波列的存在性，对模型中任意正整数n都具有普适性。在此过程中，得到了一个有趣的例子，即从其Jacobi矩阵具有一个零特征值和一个非零特征值的半双曲奇点分叉的一系列极限环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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