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...

A good initial guess and an appropriate homotopy equation are two main factors in applications of the perturbation method. For a nonlinear oscillator, cosine function is used guess. This article recommends general approach to construction equation. Duffing oscillator adopted as example elucidate effectiveness

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...

The work is devoted to the systematic research of the periodic, quasi-periodic or chaotic oscillations and the coexistence in the nonlinear Duffing-van der Pol type dynamical systems describing processes and phenomena in nature or engineering. The achieved result is the elaboration of the basic theory for searching nonlinear effects based on the concepts of periodic skeletons, bifurcation theor...

Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s w...

The phenomenon of on-off intermittency is studied in two coupled double-well Duffing oscillators with stochastic driving. We demonstrate that by using slow harmonic modulation applied to an accessible system parameter, the intermittent chaotic attractors can be completely eliminated. The influence of noise is also investigated. Power-law scaling of the average laminar time with a critical expon...

In this investigation, two different models for coupled asymmetrical oscillators, known as, forced damped Duffing oscillators (FDDOs) are reported. The first model of FDDOs consists a nonlinear oscillator (FDDO) with linear oscillator, while the second is composed FDDOs. Krylov–Bogoliubov–Mitropolsky (KBM) method, carried out analyzing any model. To do that, reduced to decoupled system individu...

The effect of the shape of six different periodic forces and second periodic forces on the onset of horseshoe chaos are studied both analytically and numerically in a Duffing oscillator. The external periodic forces considered are sine wave, square wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectified sine wave, and modulus of sine wave. An analytical threshold condition for the ...

This work develops a perturbation approach to the estimation and propagation of states in nonlinear dynamical systems with uncertainties in both the process model and output measurements. The state estimation error and statistical moments are propagated in time through a regular perturbation method in an artificial ordering parameter λ, while the state updating occurs through a linear update eq...