Stability of traveling waves involving turning points
Year: 2024
Type: article
Abstract: . In this paper, we consider a FitzHugh-Nagumo type equation, the critical manifolds of the corresponding traveling equation of which admit turning points. The simple pulse is a perturbation of a singular orbit consisting of two fast jumps and two slow motions. We show that the stability of traveling pulse relies on how the jump back arises, i.e., how the unstable manifold of the right critical manifold meets the stable manifold of the left one. Specially, we show that the pulse is stable if a'(wb) > 0 and unstable if a'(wb) < 0.
DOI: 10.3934/cpaa.2025018
Authors: Ji Li, Qing Yu, Qian Zhang
Institution: Huazhong University of Science and Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405583390