An oscillator whose frequency is amplitude dependent can be controlled by a drive whose frequency sweeps through a resonance with the oscillator's fundamental frequency. This phenomenon is called autoresonance, and has been previously investigated for drives with frequencies near the oscillator's fundamental or subharmonic frequencies. This paper examines autoresonance for drives at twice the f...

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

S. JEYAKUMARI, V. CHINNATHAMBI Department of Physics, Sri K.G.S. Arts College, Srivaikuntam 628 619, Tamilnadu, India., S. RAJASEKAR School of Physics, Bharathidasan University, Tiruchirapalli 620 024, Tamilnadu, India. [email protected], and M.A.F. SANJUAN Departamento de F́ısica, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain. [email protected] Abstract We ...

many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on duffing equation. analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. in this paper, the general form of duffing equation with cubic nonlinearity as well as paramet...

1.1 Characteristic phase dependance between direct forcing and parametric amplified forcing phase. Plotted is gain vs. phase at resonance for a 2.1 Simulated response of a parametrically resonant system under two driving conditions. The drive signal is shifted by pi-radians. The physical response, displacement is plotted here, is identical as driven by the two signals. Thus, phase shifting the ...

We study mechanical amplification and noise squeezing in a nonlinear nanomechanical resonator driven by an intense pump near its dynamical bifurcation point, namely, the onset of Duffing bistability. Phase sensitive amplification is achieved by a homodyne detection scheme, where the displacement detector's output, which has a correlated spectrum around the pump frequency, is down-converted by m...

We investigate the dynamic quantum tunneling between two attractors of a mesoscopic driven Duffing oscillator. We find that, in addition to inducing a remarkable quantum shift of the bifurcation point, the mesoscopic nature also results in a perfect linear scaling behavior for the tunneling rate with the driving distance to the shifted bifurcation point.

Dynamic stabilization of an unstable periodic orbit, a new interesting non-equilibrium phenomenon in driven nonlinear systems, has been experimentally observed in an electronic analog circuit of a driven double-well Duffing oscillator. We suggest that the dynamic stabilization is a generic property of driven nonlinear systems with humped potentials. q 2000 Published by Elsevier Science B.V.

A robust adaptation scheme for the delay of a continuous-time chaos control with half-period delayed feedback is presented. The phase-difference between the measured signal and the delayed measurement control is detected to adjust the delay to its optimum. The method when applied to the Lorenz and the Duffing oscillator shows high robustness. Copyright © 2002 IFAC

This paper deals with the dynamics of a model describing systems eonsisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is...