Equivariant Hopf Bifurcation in a Class of Partial Functional Differential Equations on a Circular Domain

IF 1.9 4区 数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Yaqi Chen, Xianyi Zeng, Ben Niu
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引用次数: 0

Abstract

Circular domains frequently appear in mathematical modeling in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a two-dimensional disk. The properties of these bifurcations at equilibriums are analyzed rigorously by studying the equivariant normal forms. Two reaction–diffusion systems with discrete time delays are selected as numerical examples to verify the theoretical results, in which spatially inhomogeneous periodic solutions including standing waves and rotating waves, and spatially homogeneous periodic solutions are found near the bifurcation points.

圆域上一类偏函数微分方程中的等变霍普夫分岔
圆域经常出现在生态学、生物学和化学领域的数学建模中。本文研究了二维圆盘上具有诺伊曼边界条件的偏函数微分方程的等变霍普夫分岔。通过研究等变正常形式,我们对这些分岔在平衡点处的性质进行了严格分析。为了验证理论结果,选取了两个具有离散时间延迟的反应扩散系统作为数值实例,在分岔点附近发现了包括驻波和旋转波在内的空间非均质周期解和空间均质周期解。
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来源期刊
International Journal of Bifurcation and Chaos
International Journal of Bifurcation and Chaos 数学-数学跨学科应用
CiteScore
4.10
自引率
13.60%
发文量
237
审稿时长
2-4 weeks
期刊介绍: The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.
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