Chaotic Behavior Analysis and Numerical Simulation of Rikitake Two-Disk Generator Model

2020 ◽  
Vol 09 (09) ◽  
pp. 1463-1468
Author(s):  
熙 张
Keyword(s):  
Numerical Simulation ◽  
Behavior Analysis ◽  
Chaotic Behavior ◽  
Generator Model

Quasi-Periodicity, Chaos and Coexistence in the Time Delay Controlled Two-Cell DC–DC Buck Converter

2014 ◽  
Vol 24 (10) ◽  
pp. 1450124 ◽  
Author(s):  
Karama Koubaâ ◽  
Moez Feki
Keyword(s):  
Numerical Simulation ◽  
Time Delay ◽  
Chaotic Attractor ◽  
Chaotic Behavior ◽  
Buck Converter ◽  
Design Parameters ◽  
Bifurcation And Chaos ◽  
Different Types ◽  
2D Torus ◽  
Discrete Map

In addition to border collision bifurcation, the time delay controlled two-cell DC/DC buck converter is shown to exhibit a chaotic behavior as well. The time delay controller adds new design parameters to the system and therefore the variation of a parameter may lead to different types of bifurcation. In this work, we present a thorough analysis of different scenarios leading to bifurcation and chaos. We show that the time delay controlled two-cell DC/DC buck converter may also exhibit a Neimark–Sacker bifurcation which for some parameter set may lead to a 2D torus that may then break yielding a chaotic behavior. Besides, the saturation of the controller can also lead to the coexistence of a stable focus and a chaotic attractor. The results are presented using numerical simulation of a discrete map of the two-cell DC/DC buck converter obtained by expressing successive crossings of Poincaré section in terms of each other.

Dynamics of an Electromechanical System With Angular and Ferroresonant Nonlinearities

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
D. O. Tcheutchoua Fossi ◽  
P. Woafo
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Harmonic Balance ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Electromechanical System ◽  
Bifurcation Diagrams ◽  
Oscillatory Solutions ◽  
Torsion Bar ◽  
Hysteresis Phenomena

The purpose of this paper is to study the dynamics of an electromechanical system consisting of a torsion-bar or two mechanical pumps activated by an electromotor. Oscillatory solutions showing the jump and hysteresis phenomena are obtained using the harmonic balance method and direct numerical simulation. Chaotic behavior is presented via the bifurcation diagrams and corresponding Lyapunov exponent. Some implications of the results on the applications of the devices are discussed.

scholarly journals Chaotic behavior analysis based on corner bifurcations

2009 ◽  
Vol 3 (4) ◽  
pp. 543-550 ◽  
Author(s):  
D. Benmerzouk ◽  
J.P. Barbot
Keyword(s):  
Behavior Analysis ◽  
Chaotic Behavior

scholarly journals Irregular Oscillations in a Realistic Abstract Quadratic Mass Action System

1980 ◽  
Vol 35 (3) ◽  
pp. 317-318 ◽  
Author(s):  
K.-D. Willamowski ◽  
O. E. Rössler
Keyword(s):  
Numerical Simulation ◽  
Chaotic Behavior ◽  
Variable Mass ◽  
Second Order ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Elementary Reactions ◽  
Action System

Abstract An open three-variable mass action kinetics is presented which exhibits chaotic behavior under numerical simulation. The elementary reactions of this system are at most of second order and satisfy the requirements of thermodynamics as long as the system is closed.

Chaotic behavior analysis for a type of switched systems and its chaotic control

2013 ◽  
Vol 30 (3) ◽  
pp. 235-241
Author(s):  
Wenguang Luo ◽  
Yingyuan Yu ◽  
Guangming Xie ◽  
Hongli Lan
Keyword(s):  
Behavior Analysis ◽  
Switched Systems ◽  
Chaotic Behavior ◽  
Chaotic Control

THE STATIONARY INSTABILITY IN QUASI-REVERSIBLE SYSTEMS AND THE LORENZ PENDULUM

2001 ◽  
Vol 11 (03) ◽  
pp. 591-603 ◽  
Author(s):  
M. CLERC ◽  
P. COULLET ◽  
E. TIRAPEGUI
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Chaotic Behavior ◽  
Reflection Symmetry ◽  
Reversible Systems ◽  
Lorenz Equations ◽  
Theoretical Predictions ◽  
Neutral Mode ◽  
Asymptotic Normal ◽  
Zero Frequency

We study the resonance at zero frequency in presence of a neutral mode in quasi-reversible systems. The asymptotic normal form is derived and it is shown that in the presence of a reflection symmetry it is equivalent to the set of real Lorenz equations. Near the critical point an analytical condition for the persistence of an homoclinic curve is calculated and chaotic behavior is then predicted and its existence verified by direct numerical simulation. A simple mechanical pendulum is shown to be an example of the instability, and preliminary experimental results agree with the theoretical predictions.

Shilnikov Chaos and Dynamics of a Self-Sustained Electromechanical Transducer

2000 ◽  
Vol 123 (2) ◽  
pp. 170-174 ◽  
Author(s):  
J. C. Chedjou ◽  
P. Woafo ◽  
S. Domngang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Critical Points ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
The Stability

The dynamics of a self-sustained electromechanical transducer is studied. The stability of the critical points is analyzed using the analytic Routh-Hurwitz criterion. Analytic oscillatory solutions are obtained in both the resonant and non-resonant cases. Chaotic behavior is observed using the Shilnikov theorem and from a direct numerical simulation of the equations of motion.

scholarly journals Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

2014 ◽  
Vol 24 (4) ◽  
pp. 759-770 ◽  
Author(s):  
Łukasz Korus
Keyword(s):  
Numerical Simulation ◽  
Distributed Systems ◽  
Lyapunov Method ◽  
Chaotic Behavior ◽  
Efficiency Analysis ◽  
Control Algorithms ◽  
Controlling Chaos ◽  
Qualitative And Quantitative ◽  
Spatially Distributed ◽  
Definition Of

Abstract The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.

scholarly journals 901 Numerical simulation on the chaotic behavior of a flow containing particles

2014 ◽  
Vol 2014.52 (0) ◽  
pp. _901-1_-_901-2_
Author(s):  
Hiroaki SHINJO ◽  
Shinichiro YANASE ◽  
Toshinori KOUCHI
Keyword(s):  
Numerical Simulation ◽  
Chaotic Behavior
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