229 research outputs found
Sufficient conditions for the existence of periodic solutions of the extended Duffing-Van der Pol oscillator
Altres ajuts: ICREA Academia, FEDER-UNAB-104E-378, CAPES grant 88881 and 030454/2013-01 do Programa CSFPVEIn this paper, some aspects on the periodic solutions of the extended Duffing-Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing-Van der Pol oscillator, we show that it can bifurcate one or three periodic solutions from a two-dimensional manifold filled by periodic solutions of the referred system. For each rescaling we exhibit concrete values for which these bounds are reached. Beyond that we characterize the stability of some periodic solutions. Our approach is analytical and the results are obtained using the averaging theory and some algebraic techniques
Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, bifurcation diagrams and phase portraits are given through analyzing the unfolding structure. Finally, numerical simulations are used to support theoretical analysis
The dynamics of the pendulum suspended on the forced Duffing oscillator
We investigate the dynamics of the pendulum suspended on the forced Duffing
oscillator. The detailed bifurcation analysis in two parameter space (amplitude
and frequency of excitation) which presents both oscillating and rotating
periodic solutions of the pendulum has been performed. We identify the areas
with low number of coexisting attractors in the parameter space as the
coexistence of different attractors has a significant impact on the practical
usage of the proposed system as a tuned mass absorber.Comment: Accepte
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