scholarly journals Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms

2009 ◽  
Vol 58 (4) ◽  
pp. 2147
Author(s):  
Shi Pei-Ming ◽  
Jiang Jin-Shui ◽  
Liu Bin
Keyword(s):  
Dynamical System ◽  
Approximate Solution ◽  
Nonlinear Dynamical System ◽  
Relative Rotation ◽  
Nonlinear Dynamical

scholarly journals Lyapunov-Schmidt reduction and singularity analysis of a high-dimensional relative-rotation nonlinear dynamical system

2012 ◽  
Vol 61 (19) ◽  
pp. 194501
Author(s):  
Shi Pei-Ming ◽  
Han Dong-Ying ◽  
Li Ji-Zhao ◽  
Jiang Jin-Shui ◽  
Liu Bin
Keyword(s):  
Dynamical System ◽  
Nonlinear Dynamical System ◽  
Singularity Analysis ◽  
High Dimensional ◽  
Relative Rotation ◽  
Nonlinear Dynamical

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

2010 ◽  
Vol 19 (9) ◽  
pp. 090306 ◽  
Author(s):  
Shi Pei-Ming ◽  
Han Dong-Ying ◽  
Liu Bin
Keyword(s):  
Dynamical System ◽  
Parametric Excitation ◽  
Nonlinear Dynamical System ◽  
Relative Rotation ◽  
Nonlinear Dynamical ◽  
Chaotic Control

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

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