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...

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

By introducing Colpitts oscillator as a chaotic system, this paper deals with back-stepping control method and investigates the restrictions and problems of the controller where non-existence of a suitable response in the presence of uncertainty is the most important problem to note. In this paper, the back-stepping sliding mode method is introduced as a robust method for controlling nonlinear ...

the dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and poincar'{e} sections. also, we employed perturbation methods such as lindstedt's method to obtain the frequency-amplitude relation of escape oscillator.

in this paper, solution of nonlinear optimal control problems and the controlled duffing oscillator, as a special class of optimal control problems, are considered and an efficient algorithm is proposed. this algorithm is based on state parametrization as a polynomial with unknown coefficients. by this method, the control and state variables can be approximated as a function of time. also, the ...

in the present paper the behavior of an elastically mounted cylinder in low and high mass-damping ratio is investigated. for high mass-damping ratio, a classical wake oscillator model is used. at the first, by neglecting all damping and nonlinear terms of this model, the possibility of using a linear model for determination of the lock-in range and the dominant mode is investigated. then, witho...

The El Niño-Southern Oscillation (ENSO) is an interannual phenomenon involved the tropical Pacific Ocean-atmosphere interactions. The oscillatory nature of ENSO requires both positive and negative ocean-atmosphere feedbacks. The positive feedback is dated back to Bjerknes' hypothesis in the 1960s, and different negative feedbacks have been proposed since the 1980s associated with the delayed os...