Adaptive oscillators are a type of nonlinear oscillator that capable learning and storing information in plastic states. Here, typical mechanical pendulum is modified to have an adjustable rod length create adaptive frequency oscillator. Since the resonance function length, this allows learn encode from external source. An experimental designed constructed, its performance compared numerical si...

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 ...

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...