Open AccessHopf bifurcation and chaotification of Josephson junction with linear delayed feedback
Author(s) -
Lisen Zhang,
Cai Li,
Feng Chao-Wen
Publication year - 2011
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.60.060306
Subject(s) - hopf bifurcation , period doubling bifurcation , biological applications of bifurcation theory , transcritical bifurcation , bifurcation , bifurcation diagram , pitchfork bifurcation , josephson effect , saddle node bifurcation , control theory (sociology) , nonlinear system , mathematics , instability , physics , mathematical analysis , mechanics , computer science , superconductivity , quantum mechanics , control (management) , artificial intelligence
In this paper, a resistive-capacitive-shunted Josephson junction with linear delayed feedback is considered. The stability of trivial solution of the controlled system is analyzed using nonlinear dynamics theory, and the theoretical results show that the stable trivial solution of the system will lose its stability via Hopf bifurcation as control parameter varies. The critical parameter condition of Hopf bifurcation is also derived. Numerical analysis of the controlled system is carried out under different parameter conditions, and the results show that the stable periodic solution generated by supercritical Hopf bifurcation may transit to chaos gradually through a process of symmetry-breaking bifurcation and period-doubling bifurcation.