In this paper, we prove the boundedness of all solutions for the equation x + n 2 x + φ(x) + g (x)q(t) = 0, where n ∈ N, q(t) = q(t + 2π), φ(x) and g(x) are bounded.

In this study, a novel analytical solution to the integrable undamping Duffing equation with constant forced term is obtained. Also, new approximate (semianalytical) for nonintegrable linear damping oscillator reported. The given in terms of Weierstrass elliptic function arbitrary initial conditions. With respect it, semianalytical constructed depending on ansatz and exact standard (in absence ...

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

this paper presents a new observer-based control scheme for a class of nonlinear systems. in the proposed method, nonlinear observer and twisting algorithm controller are employed to realize a sensor-less control strategy for complex systems which makes use of non measurable process information instead of installing as many sensors as possible. due to lack of availability of the complex system ...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...