In this paper, closed-form analytical equations for the time-domain amplitude of the MOS cross-coupled oscillators are derived. The procedure of the paper is based on estimating an accurate equation for describing the behavior of the cross-coupled MOS configurations and finding a reasonable solution for the nonlinear differential equation governing the circuit. The solution method is presented ...

We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips, frequency suppression, multiple periodic states and chaos. Such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relat...

The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting ...

A good initial guess and an appropriate homotopy equation are two main factors in applications of the perturbation method. For a nonlinear oscillator, cosine function is used guess. This article recommends general approach to construction equation. Duffing oscillator adopted as example elucidate effectiveness

‎Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated‎. ‎In this paper‎, ‎we propose RELMs with a stable online learning algorithm for the identification of continuous-time nonlinear systems in the presence of noises and uncertainties‎, ‎and we prove the global ...

in this paper, a practical review of the adomian decomposition method, to extend the procedure to handle the strongly nonlinear problems under the mixed conditions, is given and the convergence of the algorithm is proved. for this respect, a new and simple way to generate the adomian polynomials, for a general nonlinear function, is proposed. the proposed procedure, provides an explicit formula...

The current paper presents the first treatment to obtain solution of a complex Helmholtz–Duffing oscillator. This model has described elevation surface waves in fluid mechanics. non-perturbative approach is used convert nonlinear oscillator linear derive opened path for new way study more waves.

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy ...