Abstract This paper proposes a technique to identify nonlinear dynamical systems with time delay. The sparse optimization algorithm is extended proposed combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation preprocessing signals filter the noise removing dependence on initial conditions. We further integrate bootstrapping resampling ...

The paper contains technical details and proofs of recent results developed by the author, regarding the design of LPV controllers directly from experimental data. A numerical example is also presented, about control of the Duffing oscillator.

In the present paper, a new analytical technique is introduced for obtaining approximate periodic solutions of Helmholtz-Duffing oscillator. Modified Harmonic Balance Method (MHBM) is adopted as the solution method. A classical harmonic balance method does not apply directly for solving Helmholtz-Duffing oscillator. Generally, a set of difficult nonlinear algebraic equations is found when MHBM ...

The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obt...

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.

• Deduced the mechanics of hearing at low sound pressure levels from measurements of basilar membrane motion. The mechanical properties of individual sections of the cochlea have been determined by examining their collective response to tones of different frequency. The conclusion is that each section acts like a harmonic oscillator with negative damping. The oscillator is controlled by negativ...

Parametrically excited oscillators are used in several domains, particular to improve the dynamical behaviour of systems like case parametric amplification or energy harvesting. Although dry friction is often omitted during system modelling due complexity its nonsmooth nature, it sometimes necessary account for this kind damping adequately represent motion. In paper, proposed investigate effect...

Four fractal nonlinear oscillators (The Duffing oscillator, attachment Toda and a oscillator) are successfully established by He’s derivative in space, their variational principles obtained semi-inverse transform method. The approximate frequency of the four found simple formula. results show formula is powerful tool to class oscillators.

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequencyamplitude modulat...

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...