Shahid Bahonar University of Kerman Journal of Mahani Mathematical Research 2251-7952 13 1 2023 11 01 Bifurcation of big periodic orbits through symmetric homoclinics‎, ‎application to Duffing equation 1 11 3668 10.22103/jmmr.2023.20343.1349 EN Liela Soleimani Department of Applied Mathematics, University of Birjand, Birjand, Iran Omid RabieiMotlagh Department of Applied Mathematics, University of Birjand, Birjand, Iran Journal Article 2022 10 09 ‎We consider a planar symmetric vector field that undergoes a homoclinic bifurcation‎. ‎In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits‎, ‎we investigate the existence of fixed points of the exterior Poincare map around these orbits‎. This Poincare map is the result of the combination of flows inside and outside the homoclinic orbits. It shows how ‎a big periodic orbit converts to two small periodic orbits by passing through a double homoclinic structure‎. Finally‎, ‎we use the results to investigate the existence of periodic solutions of the perturbed Duffing equation. https://jmmrc.uk.ac.ir/article_3668_f6ade73746875140fe9462d97bd266d8.pdf