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On periodic orbits in a slow–fast system with normally elliptic slow manifold
Author(s) -
Sourdis Christos
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2971
Subject(s) - homoclinic orbit , mathematics , slow manifold , singular perturbation , homoclinic bifurcation , mathematical analysis , perturbation (astronomy) , ordinary differential equation , manifold (fluid mechanics) , periodic orbits , differentiable function , bifurcation , invariant manifold , center manifold , differential equation , hopf bifurcation , nonlinear system , physics , mechanical engineering , quantum mechanics , engineering
In this note, we consider the bifurcation of a singular homoclinic orbit to periodic ones in a 4‐dimensional slow–fast system of ordinary differential equations, having a 2‐dimensional normally elliptic slow manifold, originally studied by Fečkan and Rothos. Assuming an extra degree of differentiability on the system, we can refine their perturbation scheme, in particular the choice of approximate solution, and obtain improved estimates. Copyright © 2013 John Wiley & Sons, Ltd.