Some novel exact solutions and approximations to the damped Duffing–Mathieu-type oscillator with cubic nonlinearity are obtained. This work is divided into two parts: in first part, some both undamped Mathieu oscillators These expressed terms of functions kind. In second equation motion Duffing–Mathieu (dDME) solved using effective highly accurate approaches. approach, nonintegrable dDME reduce...

We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Mor...

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states an...

Duffing Oscillator is well known for its chaotic behaviour. This paper aims at clustering of emotions from the EEG response to external audio-visual stimulus used for excitation of a subject. The EEG signal corresponding to a specific emotive stimulus is used as an excitation input to a non-linear Duffing Oscillator dynamics, and the phase trajectory plots of the two state variables of the osci...

Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on Smale’s famous example, provide a rigorous way to study chaos in dynamical systems. The paper is devoted to constructing them in two-dimensional diffeomorphisms with the existence of transversal homoclinic saddles. We first propose an algorithm to automatically construct “horizontal” and “vertical” sides of the curv...

With the significant development in communication systems especially in the public channels through which our information travels, there are more increasing in the channels problems. The information security is the important one that should be enhanced. This paper presents a chaos-based speech scrambling system. Chaotic maps have been successfully used for large-scale data encryption such as im...

We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic bifurcation occurs when the Lyapunov exponent of the linearised system becomes positive. We deduce from a simple formula for the Lyapunov exponent the phase...