Work

Unfolding a Hopf Bifurcation in a Linear Reaction-diffusion Equation With Strongly Localized Impurity

Year: 2025

Type: article

Abstract: This paper presents a general framework to derive the weakly nonlinear stability near a Hopf bifurcation in a special class of multi-scale reaction-diffusion equations. The main focus is on how the linearity and nonlinearity of the fast variables in system influence the emergence of the breathing pulses when the slow variables are linear and the bifurcation parameter is around the Hopf bifurcation point. By applying the matching principle to the fast and slow changing quantities and using the singular perturbation theory, we obtain explicit expressions for the stationary pulses. Then, the normal form theory and the center manifold theory are applied to give Hopf normal form expressions. Finally, one of these expressions is verified by the numerical simulation.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240379

Authors: Ji Li, Qing Yu, Qian Zhang

Institutions: Huazhong University of Science and Technology, National Natural Science Foundation of China

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411533737

FWCI: 0.448

Cites:

Cited by: 1

Related to: 10