in this study, he’s variational approach (va) is used to solve the non-naturalvibrations and oscillations. the method works very well for the whole range of initial amplitudesand does not demand small perturbation. it is also sufficiently accurate to both linear and nonlinearphysics and engineering problems. we consider some examples to illustrate the effectiveness andconvenience of the method....

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

in this paper, a new analytical approach has been presented for solving strongly nonlinear oscillator problems. iteration perturbation method leads us to high accurate solution. two different high nonlinear examples are also presented to show the application and accuracy of the presented method. the results are compared with analytical methods and with the numerical solution using runge-kutta m...

The global attraction is established for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension coupled to a finite number of nonlinear oscillators: We prove that each finite energy solution converges as t → ±∞ to the set of all “nonlinear eigenfunctions” of the form φ(x)e−iωt if all oscillators are strictly nonlinear, and the distances between al...

Mathematical models of nonlinear oscillators are used to describe a wide variety of physical and biological phenomena that exhibit self-sustained oscillatory behavior. When these oscillators are strongly driven by forces that are periodic in time, they often exhibit a remarkable ‘‘mode-locking’’ that synchronizes the nonlinear oscillations to the driving force. The purpose of this paper is to d...

We study the collective properties of an array of nonlinear noisy oscillators driven by nonidentical periodic signals. We consider the case of a globally coupled array of harmonically forced, weakly nonlinear oscillators where there is a constant difference between the phases of the forcing signals applied to adjacent oscillators. This system is a prototypical model of a nonlinear phased array ...

Title of dissertation: NOISE-INFLUENCED DYNAMICS OF NONLINEAR OSCILLATORS J. Edmon Perkins, Doctor of Philosophy, 2015 Dissertation directed by: Professor Balakumar Balachandran Department of Mechanical Engineering Noise is usually considered detrimental to the performance of a system and the effects of noise are usually mitigated through design and/or control. In this dissertation, noise-influ...

This paper investigates the nonlinear observer design for mechanical systems, viz. nonlinear pendulum systems, undamped oscillators and Lienard systems. Explicitly, Sundarapandian’s Theorem (2002) for observer design for nonlinear systems is used to solve the problem of local exponential observer design for nonlinear pendulum systems, undamped oscillators and Lienard systems. Numerical examples...

The averaged equation for an arbitrary number of oscillators coupled by nonlinear coupling scheme invented by S. Nagano, is derived. This system is invented as a model of uni-cellular slime amoeba. By using the averaged equation, we investigate the synchronization characteristics of five coupled oscillators and a large number of coupled oscillators. In particular, we present the statistical pro...

Image contrast enhancement is realised by using nonlinear oscillatory theory. Two different uncoupled networks based on nonlinear oscillators have been studied. Simulators for both networks are developed and tested with very low contrasted images. Results show a possible effective area of application of nonlinear oscillators for image processing tasks.