ISSN:
1573-269X
Keywords:
Averaging
;
Duffing equation
;
bifurcation
;
resonance
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Applying the higher-order averaging method, we study the periodically forced, standard Duffing oscillator. A package of the computer algebra system, Mathematica, recently developed by the author and a coworker, is improved and used to implement the tedious but necessary computations for application of higher-order averaging. We detect many types of subharmonic, superharmonic and ultra-subharmonic motions and their bifurcations. A theoretical exposition for a previous numerical observation of a superstructure of bifurcation sets is partly given. A numerical example is also presented and the theoretical predictions are compared with the corresponding simulation results.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008371723533
