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Research Article | Open Access

Singular Hopf bifurcation in singularly perturbed system with delay

Xin Ai, Yue Zhang( )
College of Sciences, Northeastern University, Shenyang 110004, China
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Abstract

In this paper, we study the singular Hopf bifurcation in a class of singularly perturbed systems with delay. The key condition for the generation of a singular Hopf bifurcation involves the existence of eigenvalues of the singular pure imaginary part. The necessary and sufficient conditions for the generation of a singular Hopf bifurcation are discussed in a class of general nonlinear ( n , 1 )-fast-slow systems with delay on slow variables ( n ≥ 1 ).

Keywords

singularly perturbed systemdelaysingular Hopf bifurcation

References

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Electronic Research Archive
Volume 33 Issue 11,
November 2025
Pages 7198-7215
DOI: 10.3934/era.2025318

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Cite this article:
Ai X, Zhang Y. Singular Hopf bifurcation in singularly perturbed system with delay. Electronic Research Archive, 2025, 33(11): 7198-7215. https://doi.org/10.3934/era.2025318

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Received: 27 July 2025
Revised: 08 October 2025
Accepted: 31 October 2025
Published: 27 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)