Bifurcation of big periodic orbits through symmetric homoclinics, application to Duffing equation
عنوان مقاله: Bifurcation of big periodic orbits through symmetric homoclinics, application to Duffing equation
شناسه ملی مقاله: JR_KJMMRC-13-1_001
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_KJMMRC-13-1_001
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
Liela Soleimani - Department of Applied Mathematics, University of Birjand, Birjand, Iran
Omid RabieiMotlagh - Department of Applied Mathematics, University of Birjand, Birjand, Iran
خلاصه مقاله:
Liela Soleimani - Department of Applied Mathematics, University of Birjand, Birjand, Iran
Omid RabieiMotlagh - Department of Applied Mathematics, University of Birjand, Birjand, Iran
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.
کلمات کلیدی: Poincare map, homoclinic bifurcation, Fixed point, periodic solution
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1821786/