In this investigation, two different models for coupled asymmetrical oscillators, known as, forced damped Duffing oscillators (FDDOs) are reported. The first model of FDDOs consists a nonlinear oscillator (FDDO) with linear oscillator, while the second is composed FDDOs. Krylov–Bogoliubov–Mitropolsky (KBM) method, carried out analyzing any model. To do that, reduced to decoupled system individu...

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This study utilized combination of phase plots,time steps distribution and adaptive time steps Runge-Kutta and f if th order algorithms to investigate a harmonically Duff ing oscillator.The object is to visually compare fourth and f if th order Runge-Kutta algorithms performance as tools for seeking the chaotic solutions of a harmonically excited Duffing oscillator.Though fif th order algorithm...

This paper introduces a numerical technique for the estimation of stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise excitation. The Wiener-Hermite expansion is integrated with the Grunwald-Letnikov approximation in case of fractional order damping and with Coimbra approximation in case of variableorder damping. The numerical solver...

The use of finite-dimensional linear time-invariant controllers for the stabilization of periodic solutions in sinusoidally forced nonlinear systems is investigated. By mixing results concerning absolute stability of nonlinear systems and robustness of linear systems, a linear matrix inequality-based controller synthesis technique is developed. The synthesis algorithm yields the controller maxi...

This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping. A first order actuator ...

An accurate frequency of the Helmholtz–Duffing oscillator is obtained by a sophisticated modification He’s formulation. The pull-down instability existing in symmetric breaking phenomenon newly discovered dynamic motion for oscillators with even nonlinearities. A criterion predicting asymmetrical amplitude and built measuring change. good matching performance between analytic results numerical ...

Abstract To suppress the nonlinearity of an excited Van der Pol–Duffing oscillator (VdPD), time-delayed position and velocity are used throughout this study. The time delay is supplemental to prevent nonlinear vibration considered system. topic work extremely current because technologies with a have been subject several studies in latest days. classical homotopy perturbation method (HPM) utiliz...

Nonlinear systems exhibit a rich variety of different long-term behaviors such as: fixed points, limit cycles, quasiperiodic and chaotic behavior. In a complex system several attractors may coexist for a given set of system parameters. This coexistence is termed multistability and has been found in almost all research areas of natural science, such as: mechanics, electronics, biology, environme...

I. Serban,1,2,3 M. I. Dykman,4,* and F. K. Wilhelm1,† 1IQC and Deptartment of Physics and Astronomy, University of Waterloo, 200 University Avenue W, Waterloo, Ontario N2L 3G1, Canada 2Department Physik, Arnold-Sommerfeld-Center for Theoretical Physics, and Center for Nanoscience, Ludwig-Maximilians-Universität, Theresienstrasse 37, D-80333 München, Germany 3Instituut Lorentz, Leiden University...