This work presents a new technique to securely transmit and retrieve a message signal via chaotic systems. In our system, a two-valued message signal modulates the frequency of a Duffing oscillator sinusoidal term. An observer is used in the receiver side to retrieve the sinusoidal signal that contains the message and a novel frequency estimator is then used to reproduce an approximated estimat...

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...

Abstract Purpose In the work there are presented results of synthesis and additional validation previously developed mathematical models two different mechanical oscillators with 1 degree freedom harmonic excitation: (i) magnetically modified elasticity generating a double symmetrical minimum potential; (ii) linear springs one-sided limiter motion. Methods first case, original non-linear magnet...

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 problem of hybrid chaos synchronization is investigated, where a digital response subsystem is designed to synchronize with an analog drive subsystem. The approach taken is a new prediction-based digital redesign for a continuous-time observer embedded in the response via an optimal linearization approach of the nonlinear chaotic systems. Three typical but topologically quite different chao...

In this paper, we study the traveling wave solutions of fractional generalized reaction Duffing equation, which contains several nonlinear conformable time equations. By dynamic system method, phase portraits equation are given, and all possible exact obtained.

We propose a mean-field approach to the Duffing oscillator to construct perturbatively the bounded operators that generate the quantum states, and to define a non-Gaussian density operator. 1 The Duffing oscillator is a typical anharmonic oscillator whose classical aspect is relatively well-understood [1]. It has been studied in many fields of physics from classical mechanics to quantum mechani...