In the present effort, a data-driven modeling approach is undertaken to forecast aperiodic responses of non-autonomous systems. As representative system, harmonically forced Duffing oscillator considered. Along with it, an experimental prototype studied. Data corresponding chaotic motions are obtained through simulations oscillators hardening and softening characteristics experiments bistable o...

The present work attracts attention to obtaining a new result of the periodic solution damped nonlinear Duffing oscillator and Klein–Gordon equation. It is known that frequency response equation in can be derived from homotopy analysis method only absence damping force. We suggest suitable scheme successfully produce without losing coefficient. novel strategy centered on establishing an alterna...

A general energy-based theory of autoresonance (self-sustained resonance) in low-dimensional nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. The theory is applied to Duffing-like systems to obtain exact analytical expressions for autoresonance e...

Solving nonlinear oscillations is a challenging task due to the mathematical complexity of related differential equations. In many cases, determining oscillation’s period requires solution complicated integrals using numerical methods. To avoid complexity, there are empirical equations in literature that can be used instead rigorous analysis provide an acceptable approximation. this paper, rece...

This paper deals with the dynamics of a model describing systems eonsisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is...