scholarly journals A Postverification Method for Solving Forced Duffing Oscillator Problems without Prescribed Periods

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hong-Yen Lin ◽  
Chien-Chang Yen ◽  
Kuo-Ching Jen ◽  
Kang C. Jea
Keyword(s):  
Numerical Simulations ◽  
Random Perturbation ◽  
Duffing Oscillator ◽  
Newton's Iteration ◽  
Small Random Perturbation ◽  
Bifurcation Problems

This paper proposes a postverification method (PVM) for solving forced Duffing oscillator problems without prescribed periods. Comprising a postverification procedure and small random perturbation, the proposed PVM improves the sensitivity of the convergence of Newton’s iteration. Numerical simulations revealed that the PVM is more accurate and robust than Kubíček’s approach. We applied the PVM to previous research on bifurcation problems.

Suppressing Chaos in a Nonideal Double-Well Oscillator Using an Based Electromechanical Damped Device

2014 ◽  
Vol 706 ◽  
pp. 25-34 ◽  
Author(s):  
G. Füsun Alişverişçi ◽  
Hüseyin Bayiroğlu ◽  
José Manoel Balthazar ◽  
Jorge Luiz Palacios Felix
Keyword(s):  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Duffing Oscillator ◽  
Vibration Energy ◽  
Vibration Absorber ◽  
Electrical System ◽  
Chaotic Vibration ◽  
System A ◽  
Ideal System ◽  
Double Well Potential

In this paper, we analyzed chaotic dynamics of an electromechanical damped Duffing oscillator coupled to a rotor. The electromechanical damped device or electromechanical vibration absorber consists of an electrical system coupled magnetically to a mechanical structure (represented by the Duffing oscillator), and that works by transferring the vibration energy of the mechanical system to the electrical system. A Duffing oscillator with double-well potential is considered. Numerical simulations results are presented to demonstrate the effectiveness of the electromechanical vibration absorber. Lyapunov exponents are numerically calculated to prove the occurrence of a chaotic vibration in the non-ideal system and the suppressing of chaotic vibration in the system using the electromechanical damped device.

Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation

2021 ◽  
pp. 2050043
Author(s):  
Jing Fu ◽  
Qixing Han ◽  
Daqing Jiang ◽  
Yanyan Yang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Necessary Conditions ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Interacting Species ◽  
Sufficient And Necessary Conditions ◽  
Global Positive Solution

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research.

Analytical Periodic Motions in a Periodically Forced, Damped Duffing Oscillator

2012 ◽  
Author(s):  
Albert C. J. Luo ◽  
Jianzhe Huang
Keyword(s):  
Numerical Simulations ◽  
Analytical Solutions ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Balance Method ◽  
Periodic Motions ◽  
Conditions Of Stability ◽  
Generalized Harmonic Balance Method

The analytical solutions of the period-1 motions for a hardening Duffing oscillator are presented through the generalized harmonic balance method. The conditions of stability and bifurcation of the approximate solutions in the oscillator are discussed. Numerical simulations for period-1 motions for the damped Duffing oscillator are carried out.

Factors Influencing Ensemble Sensitivity–Based Targeted Observing Predictions at Convection-Allowing Resolutions

2020 ◽  
Vol 148 (11) ◽  
pp. 4497-4517
Author(s):  
Aaron J. Hill ◽  
Christopher C. Weiss ◽  
Brian C. Ancell
Keyword(s):  
Random Perturbation ◽  
Ensemble Prediction ◽  
Ensemble Prediction System ◽  
Small Random Perturbation ◽  
Numerical Noise ◽  
Targeted Observations ◽  
Targeted Observation ◽  
Ensemble Systems ◽  
Short Time ◽  
Impact Predictions

AbstractEnsemble sensitivity analysis (ESA) is applied to select types of observations, in various locations and in advance of forecast convection, to systematically evaluate the effectiveness of ESA-based observation targeting for 10 convection forecasts. To facilitate the analysis, observing system simulation experiments and perfect models are utilized to generate synthetic targeted observations of temperature and pressure for future assimilation with an ensemble prediction system. Various observation assimilation experiments are carried out to assess the impacts of nonlinearity, covariance localization, and numerical noise on ESA-based observation-impact predictions. It is discovered that localization applied during data assimilation restricts targeted-observation increments onto the forecast responses of composite reflectivity and 3-hourly accumulated precipitation, making impact predictions poor. In addition, numerical noise introduced by nonlinear perturbation evolution tends to reduce the correlations between observed and predicted impacts; small, random-perturbation experiments often yielded similar impacts on forecasts as targeted observations. Nonlinearity also manifests in the observation impacts when comparing targeted observations with nontargeted, randomly chosen observations; random observations have seemingly the same impact on forecasts as targeted observations. The results, under idealized conditions and simplified ensemble configurations, demonstrate that ESA-based targeting for nonlinear convection forecasts may be most applicable at short time scales. Important implications for ESA-based targeting methods employed with real-time ensemble systems are also discussed.

Periodic Motions and Bifurcation Trees in a Parametric Duffing Oscillator

2017 ◽  
Author(s):  
Albert C. J. Luo ◽  
Haolin Ma
Keyword(s):  
Differential Equation ◽  
Numerical Simulations ◽  
Duffing Oscillator ◽  
Eigenvalue Analysis ◽  
Analytic Method ◽  
Periodic Motions ◽  
Implicit Mapping ◽  
Stability And Bifurcation

This paper studies bifurcation trees of periodic motions in a parametric, damped Duffing oscillator. From the semi-analytic method, the corresponding differential equation is discretized to obtain the implicit mapping. From implicit mapping structure, the periodic nodes of periodic motions are computed, and the bifurcation trees of period-1 to period-4 motions are presented and the corresponding stability and bifurcation are carried out by eigenvalue analysis. From the analytical predictions, numerical simulations are completed, and the trajectory, harmonic amplitudes and phases of period-1 to period-4 motions are illustrated.

Sign in / Sign up

Export Citation Format

Share Document