A modified numerical method for bifurcations of fixed points of ODE systems with periodically pulsed inputs

2014 ◽  
Vol 236 ◽  
pp. 373-383 ◽  
Author(s):  
Hsiu-Chuan Wei
Keyword(s):  
Fixed Points ◽  
Numerical Method ◽  
Ode Systems

Computing the Number of Fixed Joints on Poincare Map in Nonlinear Mathieu Equation

1993 ◽  
Author(s):  
Hisato Fujisaka ◽  
Chikara Sato
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Numerical Method ◽  
Topological Degree ◽  
Poincaré Map ◽  
Mathieu Equation ◽  
Time Varying ◽  
Poincare Map ◽  
Newton's Iteration ◽  
Combined Use

Abstract A numerical method is presented to compute the number of fixed points of Poincare maps in ordinary differential equations including time varying equations. The method’s fundamental is to construct a map whose topological degree equals to the number of fixed points of a Poincare map on a given domain of Poincare section. Consequently, the computation procedure is simply computing the topological degree of the map. The combined use of this method and Newton’s iteration gives the locations of all the fixed points in the domain.

LIMIT CYCLES OF A DOUBLE OSCILLATOR EXCITED BY DRY FRICTION

2011 ◽  
Vol 21 (10) ◽  
pp. 3043-3046 ◽  
Author(s):  
SERGEY STEPANOV
Keyword(s):  
Fixed Points ◽  
Numerical Method ◽  
Limit Cycles ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Three Dimensional ◽  
Slip Mode ◽  
Two Dimensional ◽  
Parametric Investigation ◽  
Friction Laws

A two-mass oscillator with one mass lying on the driving belt with dry Coulomb friction is considered. A numerical method for finding all limit cycles and their parametric investigation, based on the analysis of fixed points of a two-dimensional map, is suggested. As successive points for the map we chose points of friction transferred from stick mode to slip mode. These transfers are defined by two equalities and yield a two-dimensional map, in contrast to three-dimensional maps that we can construct for regularized continuous dry friction laws.

Bifurcation Control for a S.D.O.F. Nonlinear System to a Principal Parametric Resonance With Time Delay

2010 ◽  
Author(s):  
Changzhao Qian ◽  
Changping Chen ◽  
Liming Dai
Keyword(s):  
Time Delay ◽  
Nonlinear System ◽  
Fixed Points ◽  
Numerical Method ◽  
Parametric Resonance ◽  
Bifurcation Point ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Bifurcation Control ◽  
Saddle Node Bifurcation

The bifurcation and response of one-degree-of-freedom system with quadratic and cubic non-linearities to a principal parametric is investigated. Using time delay damp, the bifurcation is controlled. The method of multiple scales is used to determine the equations that describe to second order the modulation of the amplitude and phase with time about one of foci. These equations are used to determine the fixed points and their stability. Because there are some items which are time delay’s function in the bifurcation equations, changing the time delay parameters may change the bifurcation form or bifurcation point. Using numerical method, saddle-node bifurcation and transcritical bifurcation control are investigated. The result indicates that time delay controller can effectively control to this kind system.

Numerical analysis of the transmission loss of water muffler according to the two-load method

2020 ◽  
Vol 234 (20) ◽  
pp. 3982-3991
Author(s):  
Jing-feng Gong ◽  
Zhi-yuan Jiang ◽  
Ling-kuan Xuan ◽  
Bao-sheng Ying ◽  
Wei-cai Peng
Keyword(s):  
Numerical Analysis ◽  
Fixed Points ◽  
Numerical Method ◽  
Test Bench ◽  
Transmission Loss ◽  
Coupled System ◽  
Measuring Process ◽  
Loss Measurement ◽  
Test Models ◽  
Loss Prediction

A numerical method for the transmission loss prediction of the water muffler has been provided according to the measuring process of the two-load method. The commonly used acoustic loads can be applied in the proposed method. The accuracy of the proposed method has been proved by comparing the calculated transmission loss with that from the traditional direct predicting method. And then the proposed method is used to discuss effects of test bench on transmission loss measurement. The predicted transmission loss curves are consistent reasonably based on different test models. The location of monitors relative to the muffler inlet and outlet has little influence on the result. But the distance between the two monitors upstream or downstream should be controlled within a certain range based on the concerning frequency band and the main pipe diameter. It is found that modes of the coupled system consisting of the test pipes and the water cause extra peaks on the transmission loss curve. The influence can be reduced by arranging appropriate fixed points. The proposed method can be used to to explain the reasonability and validity of the test bench design.

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