Bifurcation of discontinuous limit cycles of the Van der Pol equation
نویسندگان
چکیده
In this paper, we apply the methods of B-equivalence and ψ-substitution to prove the existence of discontinuous limit cycle for he Van der Pol equation with impacts on surfaces. The result is extended through the center manifold theory for coupled oscillators. he main novelty of the result is that the surfaces, where the jumps occur, are not flat. Examples and simulations are provided to emonstrate the theoretical results as well as application opportunities. 2013 IMACS. Published by Elsevier B.V. All rights reserved.
منابع مشابه
Bautin Bifurgation of a Modified Generalized Van Der Pol-mathieu Equation
The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapu...
متن کاملA new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method
In this article, a new method is introduced to give approximate solution to Van der Pol equation. The proposed method is based on the combination of two different methods, the spectral Adomian decomposition method (SADM) and piecewise method, called the piecewise Adomian decomposition method (PSADM). The numerical results obtained from the proposed method show that this method is an...
متن کاملBifurcation of a Modified BVP Circuit Model for Neurons Generating Rectangular Waves
We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhöffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcat...
متن کاملUnited Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SYNCHRONIZATION OF DIFFUSIVELY COUPLED OSCILLATORS NEAR THE HOMOCLINIC BIFURCATION
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which o...
متن کاملAnalysis and Controlling of Hopf Bifurcation for Chaotic Van Der Pol-duffing System
Analysis and controlling of bifurcation for a class of chaotic Van der PolDuffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical value of Hopf bifurcation is investigated. Based on the center manifold theory and normal form reduction, the stability index of bifurcation solution i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematics and Computers in Simulation
دوره 95 شماره
صفحات -
تاریخ انتشار 2014