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.

The paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.

TheDuffing oscillator has become a classical paradigm for illustrating the remarkable jump phenomenon and other nonlinear behaviour [1,2]. The understanding gained on the basis of this low-order nonlinear systemhas helped in the development of reducedorder models of complex mechanical systems ranging from microscales to macroscales [3,4]. The nondimensional Duffing equation with damping and ext...

To apply effective methods to analyze and distinguish all kinds of response patterns is an important issue of nonlinear dynamics. This paper contributes to develop an alternative Poincaré section method to analyze and identify the whirl responses of a nonlinear oscillator. This integration for analyzing high-order harmonic and chaotic motions is used to integrate the distance between state traj...

We present an analytical calculation of the response a driven Duffing oscillator to low-frequency fluctuations in resonance frequency and damping. find that these parameters manifest themselves distinctively, allowing them be distinguished. In strongly nonlinear regime, amplitude phase noise due damping are attenuated, while transduction into remains order $1$. show this can seen by comparing r...

The bistablity onset due to the interaction of highto low-frequency oscillations in the Duffing oscillator is considered. It is shown that such interaction results in arising of additional bistable states, which has a lower threshold for bistability with respect to the forcing amplitude as compared to the harmonically forced oscillator. This phenomenon is illustrated by considering two examples...