The dynamics of a two-degree-of-freedom nonlinear system consisting of a grounded Duffing oscillator coupled to an essentially nonlinear attachment is examined in the present study. The underlying Hamiltonian system is first considered, and its nonlinear normal modes are computed using numerical continuation and gathered in a frequencyenergy plot. Based on these results, the damped system is th...

In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The active control technique is employed to design control functions based on Lyapunov stability theory and Routh–Hurwitz criteria so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendu...

The dynamical response of an underdamped Duffing oscillator to a quasiperiodic force is investigated in the presence and absence of very weak additive noise. Particular attention is focused on the effect of noise on the characteristics of strange nonchaotic attractors (SNAs). It is concluded that even extremely weak noise is sufficient to induce dynamical complexity in an SNA. PACS: 05.45.+b, 0...

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...

We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories LPTs . The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an...

AbstractThe paper involves thorough study of non-linear vibratory oscillators and numerical methodology to analyse and resolute the non-linear dynamical world. The study involves the analysis of non-linear oscillators like the Van der Pol Oscillator and Duffing Oscillator. Application of regular perturbation method in the oscillator is also demonstrated. The equilibrium and stability analysis o...