Bifurcation of discontinuous limit cycles of the Van der Pol equation

AKHMET, MARAT; TURAN, MEHMET

doi:10.1016/j.matcom.2013.05.002

Bifurcation of discontinuous limit cycles of the Van der Pol equation

Atıf İçin Kopyala

AKHMET M., TURAN M.

MATHEMATICS AND COMPUTERS IN SIMULATION, cilt.95, ss.39-54, 2014 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 95
Basım Tarihi: 2014
Doi Numarası: 10.1016/j.matcom.2013.05.002
Dergi Adı: MATHEMATICS AND COMPUTERS IN SIMULATION
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.39-54
Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we apply the methods of B-equivalence and psi-substitution to prove the existence of discontinuous limit cycle for the Van der Pol equation with impacts on surfaces. The result is extended through the center manifold theory for coupled oscillators. The main novelty of the result is that the surfaces, where the jumps occur, are not flat. Examples and simulations are provided to demonstrate the theoretical results as well as application opportunities. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.