In this paper, periodic motions in a periodically excited, Duffing oscillator with a time-delayed displacement are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis. The time-delayed displacement is from the feedback control of displacement. The analytical bifurcation trees of period-1 motions to chaos i...

TheDuffing oscillator has become a classical paradigm for illustrating the remarkable jump phenomenon and other nonlinear behaviour [1,2]. The understanding gained on the basis of this low-order nonlinear systemhas helped in the development of reducedorder models of complex mechanical systems ranging from microscales to macroscales [3,4]. The nondimensional Duffing equation with damping and ext...

Integral boundary conditions for evolution problems have various applications in chemical engineering, thermoelasticity, underground water flow and population dynamics, see for example [16, 17, 24]. In fact, boundary value problems involving integral boundary conditions have received considerable attention, see for instance, [3, 10], [12]–[15], [18, 19, 26] and the references therein. In a rece...

In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the comple...

Chaotic motions of a Rayleigh-Duffing oscillator with periodically external and parametric excitations are investigated rigorously. Chaos arising from intersections of homoclinic orbits is analyzed with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The chaotic feature on the system parameters is discussed. Chaotic dynamics are also compare...

Based on the Takagi-Sugeno (T-S) fuzzy model approach, this study discusses robust fault-tolerant tracking controller design for non-linear systems affected by external disturbances, uncertainties, and actuator failures. In contrast to existing results, assumes fault includes linear nonlinear terms, a state feedback is designed improve stability of system when actuators fail. Using non-quadrati...

Optically actuated Radio Frequency MEMS devices are seen to self oscillate or vibrate under illumination of sufficient strength [1]. These oscillations can be frequency locked to a periodic forcing, applied through an inertial drive at the forcing frequency, or subharmonically via a parametric drive, hence providing tunability. In a previous work [2] this MEMS device was modeled by a three dime...

We investigate the behavior of a Duffing oscillator subjected to lateral periodic forcing. In our study, we analyze a mechanical model and compare our experimental data to computer simulations of the system. We have estimated the parameters of the model ODE so that the simulations provide a reasonable approximation to the physical system. We compare time series plots, Poincaré sections, and we ...