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Volume 7, Issue 3
Normal Form for the 1:1 Resonance Problems for Delayed Reaction-Diffusion Systems

Rina Su

DOI: 10.12150/jnma.2025.1066

J. Nonl. Mod. Anal., 7 (2025), pp. 1066-1083.

Published online: 2025-05

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This article presents a direct method for calculating the normal form coefficients of a 1:1 resonant Hopf bifurcation in reaction-diffusion systems with time delay and Neumann boundary conditions. The formulas obtained in this paper can be easily implemented using a computer algebra system such as Maple or Mathematica.

  • Keywords

Normal form, 1:1 resonance, Hopf bifurcation, delayed reaction-diffusion.

  • AMS Subject Headings

34C23,35B32,37C20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1066, author = {Su , Rina}, title = {Normal Form for the 1:1 Resonance Problems for Delayed Reaction-Diffusion Systems}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {3}, pages = {1066--1083}, abstract = {

This article presents a direct method for calculating the normal form coefficients of a 1:1 resonant Hopf bifurcation in reaction-diffusion systems with time delay and Neumann boundary conditions. The formulas obtained in this paper can be easily implemented using a computer algebra system such as Maple or Mathematica.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1066}, url = {http://global-sci.org/intro/article_detail/jnma/24116.html} }
TY - JOUR T1 - Normal Form for the 1:1 Resonance Problems for Delayed Reaction-Diffusion Systems AU - Su , Rina JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 1066 EP - 1083 PY - 2025 DA - 2025/05 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1066 UR - https://global-sci.org/intro/article_detail/jnma/24116.html KW - Normal form, 1:1 resonance, Hopf bifurcation, delayed reaction-diffusion. AB -

This article presents a direct method for calculating the normal form coefficients of a 1:1 resonant Hopf bifurcation in reaction-diffusion systems with time delay and Neumann boundary conditions. The formulas obtained in this paper can be easily implemented using a computer algebra system such as Maple or Mathematica.

Su , Rina. (2025). Normal Form for the 1:1 Resonance Problems for Delayed Reaction-Diffusion Systems. Journal of Nonlinear Modeling and Analysis. 7 (3). 1066-1083. doi:10.12150/jnma.2025.1066
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