This paper analytically and numerically investigates the dynamical characteristics of a fractional Duffing–van der Pol oscillator with two periodic excitations distributed time delay. First, we consider pitchfork bifurcation system driven by both high-frequency parametric excitation low-frequency external excitation. Utilizing method direct partition motion, original is transformed into an effe...

Ambient mechanical vibrations have emerged as a viable energy source for low-power wireless sensor nodes aiming the upcoming era of the 'Internet of Things'. Recently, purposefully induced dynamical nonlinearities have been exploited to widen the frequency spectrum of vibration energy harvesters. Here we investigate some critical inconsistencies between the theoretical formulation and applicati...

We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u′′ + g1(x)u ′ + g2(x)u + g3(x)u n + g4(x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics equilibria, the Duffing oscillator and numerous dynamical systems. The present work is an overview w...