In the last decade we have witnessed exciting technological advances in the fabrication and control of microelectromechanical and nanoelectromechanical systems (MEMS&NEMS) [16, 19, 26, 54, 55]. Such systems are being developed for a host of nanotechnological applications, such as highly sensitive mass [25, 34, 67], spin [56], and charge detectors [17, 18], as well as for basic research in the m...

We study the influence of decaying perturbations on autonomous oscillatory systems in a plane under assumption that preserve equilibrium state limit system, oscillate with asymptotically constant frequency, and satisfy nonresonance condition. discuss long-term behavior perturbed trajectories neighborhood state. describe conditions perturbation parameters guarantee preservation or loss stability...

The effect of the shape of six different periodic forces and second periodic forces on the onset of horseshoe chaos are studied both analytically and numerically in a Duffing oscillator. The external periodic forces considered are sine wave, square wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectified sine wave, and modulus of sine wave. An analytical threshold condition for the ...

This paper aims to identify three electrical systems: a series RLC circuit, a motor/ generator coupled system, and the Duffing-Ueda oscillator. In order to obtain the system’s models was used the error reduction ratio and the Akaike information criterion. Our approach to handle the numerical errors was the interval arithmetic by means of the resolution of the least squares estimation. The routi...

In this paper, the dynamic characteristics of fractional Duffing system are analyzed and studied by using improved short memory principle method. This method has small amount calculation high precision, can effectively improve problem large caused order. The influence frequency change on performance is nonlinear analysis methods, such as Phase Portrait, Poincare Map Bifurcation Diagram. Moreove...

Recently the classical variational problem for a Duffing type equation received again some attention. In [1], [2], [7], some variational approaches were used in order to receive the existence of solutions for both periodic and Dirichlet type boundary value problems. Mainly direct method is applied under various conditions pertaining to at most quadratic growth imposed on the nonlinear term give...