this paper proposes a hybrid control scheme for the synchronization of two chaotic duffing oscillator system, subject to uncertainties and external disturbances. the novelty of this scheme is that the linear quadratic regulation (lqr) control, sliding mode (sm) control and gaussian radial basis function neural network (grbfnn) control are combined to chaos synchronization with respect to extern...

This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with specific attention to phase resonance and its relation amplitude resonance. To this end, different families resonances, namely primary (1:1), superharmonic (k:1), subharmonic (1:ν) ultra-subharmonic (k:ν) resonances are carefully studied using first higher-order averaging. When lag is calculated between k...

In this paper, we prove that the modified PainlevéInce (PI) equation, the force-free Duffing nonlinear type oscillator (DO) and the Lotka-Volterra (LV) nonlinear ordinary differential equation ODEs can be solved in general parametric form. The developed mathematical methodology and the extracted results, being expressed by way of new theorems including admissible functional transformations and ...

In order to identify the natural frequency of ship propulsion shafting under running condition, a multi-method approach that combines Duffing Oscillator, harmonic wavelet packet transform, and probability density function is proposed. An experimental investigation on conducted test bench, response different alignment states obtained from measured bearing vibration signal. The results show can b...

Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amp...

In this work we make a high precision numerical study of the Ehrenfest theorem using Bohmian approach, where obtain classical solutions from quantum trajectories performing averages. We analyse one-dimensional harmonic and Duffing oscillator cases, finding time-dependent Schr\"odinger equation guidance for different sets initial conditions connects these results with corresponding solutions. al...

We present an innovative adaptive, model following control scheme and apply it to control a chaotic system with unknown parameters. We illustrate the proposed approach with control of Duffing oscillator problem. The same idea is used to solve three important problems: suppression of chaos, anticontrol of chaos and chaos synchronization. We propose to use ‘approximators’ linearly parameterized b...