In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the oscillator (I) (FDCDO (I)) FDCDO (II), investigated by using effective analytical numerical approaches. For approximation, models of FDCDOs reduced to decoupled standard (FDDOs). After that, both ansatz method Krylov–Bogoliubov–Mitropolsky (KBM) app...

In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results.

We present a novel application of the successive linearisation method to the classical Van der Pol and Duffing oscillator equations. By recasting the governing equations as nonlinear eigenvalue problems we obtain accurate values of the frequency and amplitude. We demonstrate that the proposed method can be used to obtain the limit cycle and bifurcation diagrams of the governing equations. Compa...

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...

In a mechanical system x is the displacement and / is the time. We call g(x) a restoring force and ƒ(/) a forcing term. Throughout this paper f{t) will be periodic and when we speak of a periodic solution of (1) we always mean a solution having the same period as ƒ(/). If g(x) is simply a constant multiplied by x, equation (1) represents a linear oscillator. In this case the amplitude of the fo...