A modified variational approach called Global Error Minimization (GEM) method is developed for obtaining an approximate closed-form analytical solution for nonlinear oscillator differential equations. The proposed method converts the nonlinear differential equation to an equivalentminimization problem. A trial solution is selectedwith unknown parameters. Next, the GEM method is used to solve th...

The issue of synchronization has been analyzed from many points of view since it was first described in 17th century. Nowadays the theory that stands behind it is so developed, it might be difficult to understand where it all comes from. This paper reminds the key concepts of synchronization by examination of two coupled Duffing oscillators. It describes also the origins of Duffing equation and...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cub...

Abstract The chaotic system plays an important role in information communication, electrical equipment, computer cryptography and so on. In this paper, four new high-dimensional complex hyperchaotic systems are found. A new overlaying regularity to generate a new high-dimensional complex hyperchaotic system is found by overlaying a series of low-dimensional chaotic system with the Duffing chaot...

In this article, under certain parametric conditions, we study the first integrals of the Duffing-van der Pol-type oscillator equations which include the van der Pol and the Duffing oscillator systems, as particular cases. After making a series of variable transformations and applying the PrellerSinger method, we find the first integrals of the simplified equations without complicated calculati...

In this paper, based on genetic algorithm (GA) and steepest descent method (SDM), we proposed a sandwich-like algorithm for the learning of neural network to identify some chaotic systems. The chaotic systems interested in this paper are the duffing equation. Different identification schemes of neural network are used to identify the duffing equation. Simulation results show that performance of...

In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner l...

Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s w...