Related papers: Characterization in bi-parameter space of a non-id…
In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation…
The driven double-well Duffing oscillator is a well-studied system that manifests a wide variety of dynamics, from periodic behavior to chaos, and describing a diverse array of physical systems. It has been shown to be relevant in…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
Different mechanisms for the creation of strange nonchaotic attractors (SNAs) are studied in a two-frequency parametrically driven Duffing oscillator. We focus on intermittency transitions in particular, and show that SNAs in this system…
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
In the work a nonlinear Duffing oscillator is considered under impulse excitation with two ways of introduction of the random additive term simulating noise, - with help of amplitude modulation and modulation of period of impulses sequence.…
We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show…
Dynamics of the Duffing--Van der Pol driven oscillator is investigated. Periodic steady-state solutions of the corresponding equation are computed within the Krylov-Bogoliubov-Mitropolsky approach to yield dependence of amplitude $A$ on…
We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic…
The Duffing oscillator describes the dynamics of a mass suspended on a spring with position-dependent stiffness. The mass is assumed to experience a linear damping and a time-dependent external forcing. The model has been instrumental in…
We present an experimental study of the Duffing--Holmes oscillator with a double-well potential, implemented as an analog electronic circuit under periodic external forcing. By systematically varying the forcing amplitude and frequency, we…
A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic multi-stability emerges associated with…
The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…
We study the dissipative bi-stable Duffing oscillator with equal energy wells and observe fractal patterns in the parameter space of driving frequency, forcing amplitude, and damping ratio. Our numerical investigation reveals the Hausdorff…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as…
The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose dynamics are similar to those of bistable mechanical systems, such as Euler arches and Duffing…