Global dynamics of the Josephson equation in TS^1

Release time:2020-04-06

DOI number:10.1016/j.jde.2020.03.048

Journal:Journal of Differential Equations

Key Words:Limit cycle; Josephson equation; Homoclinic loop; Two-saddle loop; Saddle connection

Abstract:The Josephson equation $\dot \phi=y,~\dot y=-\sin\phi+\epsilon \big(a-(1+\gamma\cos\phi)y\big)$ was researched by Sanders and Cushman in [{\it SIAM J. Math. Anal.} {\bf 17} (1986), 495-511] for its phase portraits when $\epsilon>0$ is small by applying the averaging method. The parameter $\epsilon$ can actually be large or even any real number in the practical application of this model. When $|\epsilon|$ is not small, we cannot apply the averaging method because the system is not near-Hamiltonian. For general $\epsilon \in \mathbb{R}$, we present complete dynamics and more complex bifur

Co-author:Tang Yilei

First Author:Chen Hebai

Indexed by:Unit Twenty Basic Research

Discipline:数学

Document Type:J

Volume:269

Issue:6

Page Number:4884-4913

Translation or Not:no

Date of Publication:2020-04-06

Included Journals:SCI

Links to published journals:https://doi.org/10.1016/j.jde.2020.03.048