We study the nonlinear oscillations of a forced and weakly dissipative spring– magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the osc...

In this work, by using a simple transformation technique, we have show that the nonlinear wave equations: Zakharov equations and generalized Zakharov equations can be reduced to the same family of Duffing or double-well Duffing equations. Then by means of quotient trigonometric function expansion method, many kinds of exact and explicit solutions of this family of equations are obtained in a un...

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms ...

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...

ABSTRACT An accurate closed-form solution for the quintic Duffing equation is obtained using a cubication method. In this method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude. The replacement of the origi...

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...

This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this method, the initial value problem of the system is numerically integrated and the control parameter is switched periodically within a chosen set of parameter values. The resulted attractor matches with the attractor ...

In this paper, a super twisting controller (STC) is designed to control the chaotic behavior of the Duffing-Holmes system in stabilization and tracking cases. Due to lack of availability of the performance evaluation of STC in controlling Duffing-Holmes system, this paper aims to test the performance of STC in controlling DuffingHolmes system. In order to achieve this control design, a modifica...

We have studied experimentally a chaotic cryptosystem, which is based on the inverse system approach. We applied this method to a second order nonlinear circuit (master circuit), which is described by a Duffing equation. We present the implementation of the slave circuit with the inverse system approach and we demonstrate the decryption when the information signal has several forms (sinusoidal ...

Duffing systems excited by harmonic excitations and subjected to noise additions are considered, it is examined whether the addition can be used steer response from one stable mode another. To help with this examination, authors propose a methodology for estimating probability that short duration Gaussian white generate or destroy modes of single nonlinear oscillator as well set coupled oscilla...