Entry–Exit Functions in Fast–Slow Systems with Intersecting Eigenvalues

• Published in: Journal of dynamics and differential equations Vol. 37; no. 1; pp. 559 - 576
• Main Authors: Kaklamanos, Panagiotis, Kuehn, Christian, Popović, Nikola, Sensi, Mattia
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2025; Springer Nature B.V; Springer Verlag
• Subjects: Applications of Mathematics; Differential equations; Eigenvalues; Fields (mathematics); Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Real variables; Stability; Transcritical bifurcation; Fast–slow systems; Ordinary differential equations; Entry–exit function; Geometric singular perturbation theory; Secondary 34A26; 34C60; Delayed loss of stability; Primary 34C23; 34E15
• ISSN: 1040-7294; 1572-9222
• DOI: 10.1007/s10884-023-10266-2

We study delayed loss of stability in a class of fast–slow systems with two fast variables and one slow one, where the linearisation of the fast vector field along a one-dimensional critical manifold has two real eigenvalues which intersect before the accumulated contraction and expansion are balanc...