Work

Transverse Bifurcations Occurring on Simple Robust Homoclinic Cycles

Year: 2026

Type: article

Abstract: This paper studies codimension-one transverse bifurcations of several classes of simple robust homoclinic cycles in group-symmetric systems on R5. The analysis follows a complete classification induced by the representation of the symmetric group. Sufficient conditions are established under which new homoclinic cycles or heteroclinic connections bifurcate from the original cycle. An asymptotic expansion of the Poincaré map is derived, yielding explicit criteria for the bifurcation of periodic orbits from such homoclinic cycles and for determining their stability.

Source: Mathematics

DOI: 10.3390/math14163012

Authors: Yanqi Zhang, Cuiping Li, Kunlun Huang, Xiao Wen

Institution: Beihang University

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China