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

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...