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 nonlinear equations of motion such as the Duffing oscillator equation and its family are seldom addressed in intermediate instruction classical dynamics; this one is problematic because it cannot be solved terms elementary functions before. Thus, work, stability analysis quadratic damping higher-order nonlinearity investigated. Hereinafter, some new analytical solutions to undamped form Wei...

The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...

We investigate the dynamics of small-scale turbulence-driven sheared E B ows in nonlinear gyroouid simulations. The importance of these zonal ows in the regulation of the turbulence was shown in our early simulations 1{3 and has been widely connrmed. Most of these ows experience fast collisionless linear damping, but there is a residual non-Maxwellian component of the ow which is undamped 4 and...

In this investigation, some analytical solutions to both conserved and non-conserved rotational pendulum systems are reported. The exact solution the oscillator (unforced, undamped oscillator), is derived in form of a Jacobi elliptical function. Moreover, an approximate for case obtained trigonometric A comparison between examined. approximations oscillators including unforced, damped forced, o...

Context. Standing transverse oscillations of coronal loops are observed to operate in two regimes: rapidly decaying, large amplitude oscillations and undamped small amplitude oscillations. In the latter regime the damping should be compensated by energy supply, which allows the loop to perform almost monochromatic oscillations with almost constant amplitude and phase. Different loops oscillate ...

An oscillatory network of columnar architecture located in 3D spatial lattice was recently designed by the authors as oscillatory model of the brain visual cortex. Single network oscillator is a relaxational neural oscillator with internal dynamics tunable by visual image characteristics - local brightness and elementary bar orientation. It is able to demonstrate either activity state (stable u...

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...

While consistency of the maximum likelihood estimator of the drift matrix in a multi-dimensional continuous time Ornstein-Uhlenbeck process holds under rather general conditions, little is known about the rate of convergence and the limiting distribution of the estimator when the underlying process is not ergodic. The objective of the paper is to investigate these questions for an important exa...

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...