In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this...

Four fractal nonlinear oscillators (The Duffing oscillator, attachment Toda and a oscillator) are successfully established by He’s derivative in space, their variational principles obtained semi-inverse transform method. The approximate frequency of the four found simple formula. results show formula is powerful tool to class oscillators.

We have studied experimentally a chaotic cryptosystem, which is based on the inverse system approach. We applied this method to a second order nonlinear circuit (master circuit), which is described by a Duffing equation. We present the implementation of the slave circuit with the inverse system approach and we demonstrate the decryption when the information signal has several forms (sinusoidal ...

In this paper,we introduce a piecewise variational iterationmethod for treating a nonlinear oscillator of a mass attached to a stretched elastic wire. For the nonlinear oscillator, the present method can produce a good approximation to the exact solution in a very large region, while the standard variational iteration method (VIM) gives a good approximation only in a small region. The numerical...

The aim of this comment is to extend the study of the dynamics of a finite extensibility nonlinear oscillator conducted by Febbo [M. Febbo, A finite extensibility nonlinear oscillator, Applied Mathematics and Computation 217 (2011) 6464-6475]. We show that the linearized harmonic balance method is not sufficiently adequate for this oscillator and that the harmonic balance method without lineari...

A glottal model based on physical constraints is proposed. The model describes the vocal fold as a simple oscillator, i.e. a damped mass-spring system. The oscillator is coupled with a nonlinear block, accounting for fold interaction with the airflow. The nonlinear block is modelled as a regressor-based functional with weights to be identified, and a pitch-synchronous identification procedure i...

The circle map and its basic properties as non-linear oscillator are discussed and related to other iterative mappings as proposed in the literature. The circle map is the simplest iterative generator for sustained periodic and chaotic sounds and is easy to interpret as a basic sine oscillator with a nonlinear perturbation.

Protein ubiquitination and degradation play important roles in many biological functions and are associated with many human diseases. It is well known that for biochemical oscillations to occur, proper degradation rates of the participating proteins are needed. In most mathematical models of biochemical reactions, linear degradation kinetics has been used. However, the degradation kinetics in r...

Abstract. In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, ẍ+αxẋ+βx+γx = 0,which preserves the form of the time independent integral, conservative Hamiltonian and the equation of motion. Generalizing this transformation we prove the existence of non...

We study the effect of a randomly modulated harmonic driving on the phase behavior of a nonlinear oscillator. A multiple-scale analysis shows that the system is formally equivalent to a rocked oscillator, in which a modulated harmonic driving locks the system at one of two phases, both of which are in quadrature with that of the driving. This theoretically predicted noise-induced bistable phase...