We have studied experimentally the inverse system approach, which is used when we want to synchronize two chaotic systems (master – slave). We apply this method to a second order nonlinear circuit, which is described by a Duffing equation. We present two different implementations of the slave circuit with the inverse method and we demonstrate the possibility of synchronization when the two circ...

We use a direct variational method in order to investigate the dependence on parameter for the solution for a Duffing type equation with Dirichlet boundary value conditions. Mathematics Subject Classification. 49J02

This study addresses the problem of predicting convergence outcomes in Duffing equation, a nonlinear second-order differential equation. The equation exhibits intriguing behavior both undamped free vibration and forced with damping, making it subject significant interest. In vibration, result oscillates randomly between 1 −1, contingent upon initial conditions. For multiple variables, including...

In this paper, we develop two wave-based approaches for predicting the nonlinear periodic response of jointed elastic bars. First, present a vibration approach (WBVA) studying systems informed by re-usable, perturbation-derived scattering functions. This analytical can be used to predict steady-state, forced bar structures incorporating any number and variety joints. As second method, Plane-Wav...

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in the paper. In order to suppress the irregular chaotic motion, an optimal backstepping controller is designed. The backstepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the syste...

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...