Geometric Singular Perturbation Analysis of the Yamada Model

DOI10.1137/040604820zbMath1106.34027OpenAlexW2055410928MaRDI QIDQ5700607

Astrid Huber, Peter Szmolyan

Publication date: 28 October 2005

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/040604820

zbMATH Keywords

homoclinic orbitslaser dynamicsblow-up methodslow-fast dynamics

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Lasers, masers, optical bistability, nonlinear optics (78A60) Qualitative investigation and simulation of ordinary differential equation models (34C60) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Relaxation oscillations for ordinary differential equations (34C26)

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Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics ⋮ Discrete geometric singular perturbation theory ⋮ The Yamada Model for a Self-Pulsing Laser: Bifurcation Structure for Nonidentical Decay Times of Gain and Absorber ⋮ Slow unfoldings of contact singularities in singularly perturbed systems beyond the standard form ⋮ BIFURCATION STRUCTURES IN A MODEL OF A CO₂ LASER WITH A FAST SATURABLE ABSORBER ⋮ Geometric singular perturbation theory in biological practice ⋮ Two-stroke relaxation oscillators ⋮ Multiscale geometry of the Olsen model and non-classical relaxation oscillations ⋮ Analysis of Interacting Local Oscillation Mechanisms in Three-Timescale Systems

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