Bifurcation of Rotating Wave Solutions in Reaction-Diffusion Systems on a Circle

Qingying Cai; Junping Shi; Ying Su

doi:10.1007/s10884-026-10519-w

Bifurcation of Rotating Wave Solutions in Reaction-Diffusion Systems on a Circle

Qingying Cai
, Junping Shi^*
, Ying Su

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology
College of William and Mary

Research output: Contribution to journal › Article › peer-review

Abstract

The existence of rotating wave solutions of a general reaction-diffusion system with nonlocal interaction on a circle are proved using a new bifurcation approach with two parameters, and a normal form for the rotating wave bifurcations is also developed to compute the direction of the bifurcation diagram. Theoretical results are applied to two model systems for the existence of rotating waves which are further verified by numerical simulations.

Original language	English
Journal	Journal of Dynamics and Differential Equations
DOIs	https://doi.org/10.1007/s10884-026-10519-w
State	Accepted/In press - 2026
Externally published	Yes

Keywords

Bifurcation
Nonlocal interaction
Reaction-diffusion
Rotating waves

Access to Document

10.1007/s10884-026-10519-w

Cite this

@article{1ffb58ad53c341c0811f6b6a43fee7a2,

title = "Bifurcation of Rotating Wave Solutions in Reaction-Diffusion Systems on a Circle",

abstract = "The existence of rotating wave solutions of a general reaction-diffusion system with nonlocal interaction on a circle are proved using a new bifurcation approach with two parameters, and a normal form for the rotating wave bifurcations is also developed to compute the direction of the bifurcation diagram. Theoretical results are applied to two model systems for the existence of rotating waves which are further verified by numerical simulations.",

keywords = "Bifurcation, Nonlocal interaction, Reaction-diffusion, Rotating waves",

author = "Qingying Cai and Junping Shi and Ying Su",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2026.",

year = "2026",

doi = "10.1007/s10884-026-10519-w",

language = "英语",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer",

}

TY - JOUR

T1 - Bifurcation of Rotating Wave Solutions in Reaction-Diffusion Systems on a Circle

AU - Cai, Qingying

AU - Shi, Junping

AU - Su, Ying

N1 - Publisher Copyright: © The Author(s) 2026.

PY - 2026

Y1 - 2026

N2 - The existence of rotating wave solutions of a general reaction-diffusion system with nonlocal interaction on a circle are proved using a new bifurcation approach with two parameters, and a normal form for the rotating wave bifurcations is also developed to compute the direction of the bifurcation diagram. Theoretical results are applied to two model systems for the existence of rotating waves which are further verified by numerical simulations.

AB - The existence of rotating wave solutions of a general reaction-diffusion system with nonlocal interaction on a circle are proved using a new bifurcation approach with two parameters, and a normal form for the rotating wave bifurcations is also developed to compute the direction of the bifurcation diagram. Theoretical results are applied to two model systems for the existence of rotating waves which are further verified by numerical simulations.

KW - Bifurcation

KW - Nonlocal interaction

KW - Reaction-diffusion

KW - Rotating waves

UR - https://www.scopus.com/pages/publications/105041474306

U2 - 10.1007/s10884-026-10519-w

DO - 10.1007/s10884-026-10519-w

M3 - 文章

AN - SCOPUS:105041474306

SN - 1040-7294

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

ER -

Bifurcation of Rotating Wave Solutions in Reaction-Diffusion Systems on a Circle

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this