In the present study, several successive approximate solutions of nonlinear oscillator are derived by using efficient frequency formula. A systematical analysis formulation helps to establish a general periodic solution. Each approximation represents, individually, solution oscillator. For optimal design and accurate prediction structural behavior, new optimizer is demonstrated for solutions. T...

In [17] it was suggested that the number of limit cycles in a piecewise-linear system could be closely related to the number of zones, that is the number of parts of the phase plane where the system is linear. In this note we construct an example of a class of perturbed piecewise systems with n zones such that the first variation of the displacement function is identically zero. Then we conject...

This paper introduces a wavelet-based linearization method to estimate the single-degree-of-freedom (SDOF) nonlinear system response based on the traditional equivalent linearization technique. The mechanism by which the signal is decomposed and reconstructed using the wavelet transform is investigated. Since the wavelet analysis can capture temporal variations in the time and frequency content...

A critical hurdle of a nonlinear vibration system in fractal space is the inefficiency modelling system. Specifically, differential equation models cannot elucidate effect porosity size and distribution periodic property. This paper establishes fractal-differential model for this purpose, Duffing-Van der Pol oscillator (DVdP) with two-scale derivatives forced term considered as an example to re...

Abstract The chaotic system plays an important role in electronic and electrical equipment, computer cryptography, computer communication and so on. In this paper, we established three new six-dimensional complex chaotic systems and one new ten-dimensional complex chaotic system. The regularity to generate high-dimensional chaotic system is also found by overlaying a series of low-dimensional c...