Geometric Singular Perturbation and Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".
Deadline for manuscript submissions: 31 July 2026
Special Issue Editor
Interests: differential equations; dynamical systems; variational methods and applications; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
The geometric singular perturbation theory (GSPT), which plays an important part in characterizing the influence of small parameters on dynamical systems in practical applications, has been applied in various fields, such as engineering, economics, biology, and thermodynamics. It enables us to investigate dynamic systems with different time scales while providing robust solutions to singular perturbation challenges.
This Special Issue aims to highlight the application of GSPT in addressing real-world challenges, with a focus on traveling wave solution techniques. We welcome high-quality submissions encompassing survey articles covering, but are not limited to, the following fields:
- Theoretical developments in GSPT for degenerate systems;
- Time-delay systems;
- Applications of bifurcation theory to wave stability;
- Computational methods for constructing slow manifolds;
- Interplay between GSPT and biological models;
- The existence of limit cycles under small perturbation.
We warmly invite researchers to submit original works exploring innovative analytical frameworks for singular perturbation problems, particularly those bridging theory with applications in epidemic systems, predator–prey models, and physical systems. We especially courage interdisciplinary research that develops multiscale modeling frameworks that address forefront scientific challenges worldwide.
Dr. Yu Tian
Guest Editor
Manuscript Submission Information
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Keywords
- geometric singular perturbation theory
- fast–slow system
- invariant manifold theorem
- Fenichel's theorems
- bifurcation theory
- exchange lemma
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