We find an upper bound for the number of limit cycles, bifurcating from eight-loop Duffing oscillator $$x''= x-x^{3}$$ under special cubic perturbation $$\begin{aligned} x''= x-x^{3}+\lambda _{1}y+\lambda _{2}x^{2}+\lambda _{3}xy+\lambda _{4}x^{2}y. \end{aligned}$$

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...

Some novel exact solutions and approximations to the damped Duffing–Mathieu-type oscillator with cubic nonlinearity are obtained. This work is divided into two parts: in first part, some both undamped Mathieu oscillators These expressed terms of functions kind. In second equation motion Duffing–Mathieu (dDME) solved using effective highly accurate approaches. approach, nonintegrable dDME reduce...