We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.

We study the periodic solutions of the following kind of non-autonomous Duffing differential equation ÿ+ay− εy = εh(t, y, ẏ), with a > 0, ε a small parameter and h a C2 function in its variables.

By using Mawhin–Manásevich continuation theorem, some new sufficient conditions for the existence and uniqueness of periodic solutions of Duffing type p-Laplacian differential equation are established, which are complement of previously known results. © 2007 Elsevier Inc. All rights reserved.

In this work, we propose a novel phenomenological model of the EEG signal based on the dynamics of a coupled Duffing-van der Pol oscillator network. An optimization scheme is adopted to match data generated from the model with clinically obtained EEG data from subjects under resting eyes-open (EO) and eyes-closed (EC) conditions. It is shown that a coupled system of two Duffing-van der Pol osci...

In recent years, many authors are greatly attached to investigation for the existence and uniqueness of solution of Duffing equations, for example, 1–11 , and so forth. Some authors 8, 11, 12 , etc. proved the existence and uniqueness of solution of Duffing equations underC2 perturbation functions and other conditions at nonresonance by employingminimax theorems. In 1986, Tersian investigated t...

Ambient mechanical vibrations have emerged as a viable energy source for low-power wireless sensor nodes aiming the upcoming era of the 'Internet of Things'. Recently, purposefully induced dynamical nonlinearities have been exploited to widen the frequency spectrum of vibration energy harvesters. Here we investigate some critical inconsistencies between the theoretical formulation and applicati...

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequencyamplitude modulat...

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

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...