scholarly journals Numerical Bifurcation Analysis of a Piecewise-Smooth Nonlinear Oscillator System With Impacts

2021 ◽  
Author(s):  
Brian Saunders ◽  
Rui Vasconcellos ◽  
Robert Kuether ◽  
Abdessattar Abdelkefi
Keyword(s):  
Bifurcation Analysis ◽  
Nonlinear Oscillator ◽  
Piecewise Smooth ◽  
Oscillator System ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

Numerical bifurcation analysis framework for autonomous piecewise-smooth dynamical systems

2009 ◽  
Vol 42 (1) ◽  
pp. 187-201 ◽  
Author(s):  
Quentin Brandon ◽  
Tetsushi Ueta ◽  
Danièle Fournier-Prunaret ◽  
Takuji Kousaka
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Piecewise Smooth ◽  
Analysis Framework ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

Numerical Bifurcation Analysis of Delayed Recycle Stream in a Continuously Stirred Tank Reactor

2010 ◽  
Author(s):  
Nalwala Rohitbabu Gangadhar ◽  
Periyasamy Balasubramanian ◽  
Swapan Paruya ◽  
Samarjit Kar ◽  
Suchismita Roy
Keyword(s):  
Bifurcation Analysis ◽  
Stirred Tank ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Continuously Stirred Tank Reactor ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

scholarly journals Numerical bifurcation analysis of a ?car-following? model

PAMM ◽  
2004 ◽  
Vol 4 (1) ◽  
pp. 552-553
Author(s):  
Gabriele Sirito ◽  
Ingeniun Gasser ◽  
Tilman Seidel
Keyword(s):  
Bifurcation Analysis ◽  
Car Following ◽  
Car Following Model ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

Numerical Bifurcation Analysis of Multimode Impact Oscillations Between a Pantograph and a Rigid Conductor Line

2012 ◽  
Author(s):  
Kiyotaka Yamashita ◽  
Tomoaki Nakayama ◽  
Toshihiko Sugiura ◽  
Hiroshi Yabuno
Keyword(s):  
Bifurcation Analysis ◽  
Numerical Technique ◽  
Single Mode ◽  
Current Collection ◽  
Conductor Line ◽  
Mode Solution ◽  
Numerical Bifurcation ◽  
The Impact ◽  
Impact Oscillations ◽  
Numerical Bifurcation Analysis

This paper deals with the numerical bifurcation analysis of the contact loss between a pantograph and an overhead rigid conductor line in a railway current collection system. In the previous study, we modeled this problem as impact oscillations of an intermediate spring-supported beam excited by an oscillating plate. We have already derived the modal interaction relationship equations that describe the velocities immediately after an impact as functions of the velocities before impact for each vibration mode. A numerical calculation using these relationship equations was performed to clarify the impact oscillations with multiple vibration modes. In this paper, we propose a numerical technique based on maps that transform the state of the system at the impact to the subsequent state at the next impact. This numerical method produces stability analyses of the fixed points of the map that describes an impact oscillation with multiple modes. These results can differ surprisingly from the expectations based on a single-mode solution. These results are compared with experiments undertaken in our laboratory, utilizing a thin stainless steel beam. The typical features of impact oscillations, which were theoretically predicted, were confirmed qualitatively.

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