Periodic solutions of a harmonically forced Duffing oscillator with time-delay state feedback are investigated using the incremental harmonic balance method. In process solving, explicit effect matrix time delay term was derived. The stability periodic determined by method which combines continuous approximation and multivariable Floquet theory. On this basis, frequency–amplitude response curve...

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order RungeKutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is a...

Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1-d bidirectional Maxwell equations. This system of equations has a one parameter family of exact anal...

an asymptotically stable direct adaptive fuzzy pi sliding modecontroller is proposed for a class of nonlinear uncertain systems. in contrast toother existing approaches of handling disturbances, the proposed approachdoes not require this bound to be known, only requiring that it exists.moreover, a pi control structure is used to attenuate chattering. the approachis applied to stabilize an open-...