We study the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behavior. We study these transitions in detail for small and large numbers of oscillators. P...

Abstract This paper investigates the dynamics of a Duffing oscillator excited by an unbalanced motor. The interaction between motor and vibrating system is considered as nonideal, which means that excitation provided can be influenced response, case in general for real systems. constitutes important difference with respect to classical (ideally excited) oscillator, where amplitude frequency ext...

We study persistence of periodic and homoclinic orbits, first integrals commutative vector fields in dynamical systems depending on a small parameter $\varepsilon>0$ give several necessary conditions for their persistence. Here we treat orbits not only to equilibria but also orbits. discuss some relationships these results with the standard subharmonic Melnikov methods time-periodic perturbatio...

TheDuffing oscillator has become a classical paradigm for illustrating the remarkable jump phenomenon and other nonlinear behaviour [1,2]. The understanding gained on the basis of this low-order nonlinear systemhas helped in the development of reducedorder models of complex mechanical systems ranging from microscales to macroscales [3,4]. The nondimensional Duffing equation with damping and ext...

Abstract To suppress the nonlinearity of an excited Van der Pol–Duffing oscillator (VdPD), time-delayed position and velocity are used throughout this study. The time delay is supplemental to prevent nonlinear vibration considered system. topic work extremely current because technologies with a have been subject several studies in latest days. classical homotopy perturbation method (HPM) utiliz...