Open AccessAsymptotic Analysis of the Hopf-Hopf Bifurcation in a Time-delay System
Author(s) -
Christoffer Heckman,
Richard H. Rand
Publication year - 2012
Publication title -
journal of applied nonlinear dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.189
H-Index - 10
eISSN - 2164-6473
pISSN - 2164-6457
DOI - 10.5890/jand.2012.05.004
Subject(s) - hopf bifurcation , mathematics , control theory (sociology) , computer science , bifurcation , physics , control (management) , artificial intelligence , nonlinear system , quantum mechanics
A delay differential equation (DDE) which exhibits a double Hopf or Hopf-Hopf bifurcation [1] is studied using both Lindstedt’s method and center manifold reduction. Results are checked by comparison with a numerical continuation program (DDEBIFTOOL). This work has application to the dynamics of two interacting microbubbles.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom