Dynamics analysis of a gyrostat system with intermittent forcing

2021 ◽  
pp. 095965182110590
Author(s):  
Jianbin He ◽  
Jianping Cai
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Dynamics Analysis ◽  
Bifurcation Diagrams ◽  
Stable Point ◽  
Dynamical Characteristics ◽  
Main Work ◽  
Selection Of

The dynamical characteristics of a gyrostat system with intermittent forcing are investigated, the main work and contributions are given as follows: (1) The gyrostat system with an intermittent forcing is studied, and its dynamical characteristics are investigated by the corresponding Lyapunov exponent spectrums and bifurcation diagrams with respect to the amplitude of intermittent forcing. The modified gyrostat system exists chaotic motion when the amplitude of intermittent forcing belongs to a certain interval, and it can be at a state of stable point or periodic motion by the design of amplitude. (2) The gyrostat system with multiple intermittent forcings is also investigated through the combination of Lyapunov exponent spectrums and bifurcation diagrams, and it behaves periodic motion or chaotic motion when the amplitude or forcing width is different. (3) By the selection of parameters in intermittent forcings, the modified gyrostat system is at a state of stable point, periodic motion or chaotic motion. Numerical simulations verify the feasibility and effectiveness of the modified gyrostat system.

Experimental Study of a Symmetrical Piecewise Base-Excited Oscillator

1998 ◽  
Vol 65 (3) ◽  
pp. 657-663 ◽  
Author(s):  
M. Wiercigroch ◽  
V. W. T. Sin
Keyword(s):  
Experimental Study ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Piecewise Linear ◽  
Calibration Procedure ◽  
Experimental Setup ◽  
Stiffness Ratio ◽  
Bifurcation Diagrams ◽  
Parameter Values ◽  
Excited Oscillator

This paper presents an experimental study on a base-excited piecewise linear oscillator with symmetrical flexible constrains of high stiffness ratio (above 20). The details of the adopted design of the oscillator, the experimental setup, and calibration procedure are briefly discussed. The regions of chaotic motion predicted theoretically were confirmed by the experimental results arranged into bifurcation diagrams. Clearance, stiffness ratio, amplitude, and frequency of the external force were used as branching parameters. The discussion of the system dynamics is based on bifurcation diagrams and Lissajous curves. The investigated system tends to be periodic for large clearances and chaotic for small ones. This picture is reversed for the amplitude of the forcing changes, where periodic motion occurred for small values and chaos dominated for larger forcing. The same behavior is observed for increasing frequency ratio where, for values below the natural frequency, the most interesting dynamics occurs. For the investigated parameter values, the stiffness ratio variation produces only periodic motion.

scholarly journals Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 474 ◽  
Author(s):  
Lazaros Moysis ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jesus M. Munoz-Pacheco ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Image Encryption ◽  
Fuzzy Numbers ◽  
Statistical Tests ◽  
Logistic Map ◽  
Simple Rule ◽  
Pseudorandom Number ◽  
Bifurcation Diagrams ◽  
Triangular Numbers ◽  
Pseudorandom Number Generation

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

scholarly journals Chaos and Control in Coronary Artery System

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yanxiang Shi
Keyword(s):  
Coronary Artery ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Road ◽  
Two Systems ◽  
And Control

Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

GENERALIZED SYNCHRONIZATION OF CHAOS IN RCL-SHUNTED JOSEPHSON JUNCTIONS BY UNIDIRECTIONALLY COUPLING

2010 ◽  
Vol 24 (29) ◽  
pp. 5675-5682 ◽  
Author(s):  
YU-LING FENG ◽  
XI-HE ZHANG ◽  
ZHI-GANG JIANG ◽  
KE SHEN
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Josephson Junctions ◽  
System Approach ◽  
Chaotic Synchronization ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Maximum Condition ◽  
Two Systems

This paper investigates chaotic synchronization in the generalized sense in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using the means of unidirectionally coupling. The numerical simulations confirm that the generalized synchronization of chaos in these two systems can be achieved with a suitable coupling intensity when the maximum condition Lyapunov exponent (MCLE) is negative. Also, the auxiliary system approach is used to detect the existence of the generalized synchronization.

Recollimation shocks in relativistic jets

2018 ◽  
Vol 27 (10) ◽  
pp. 1844011 ◽  
Author(s):  
José M. Martí ◽  
Manel Perucho ◽  
José L. Gómez ◽  
Antonio Fuentes
Keyword(s):  
Magnetic Fields ◽  
Numerical Simulations ◽  
Theoretical Background ◽  
Synchrotron Emission ◽  
Relativistic Jets ◽  
Dominant Type ◽  
X Ray ◽  
Extragalactic Jets ◽  
X Ray Binaries ◽  
Selection Of

Recollimation shocks (RS) appear associated with relativistic flows propagating through pressure mismatched atmospheres. Astrophysical scenarios invoking the presence of such shocks include jets from AGNs and X-ray binaries and GRBs. We shall start reviewing the theoretical background behind the structure of RS in overpressured jets. Next, basing on numerical simulations, we will focus on the properties of RS in relativistic steady jets threaded by helical magnetic fields depending on the dominant type of energy. Synthetic radio maps from the simulation of the synchrotron emission for a selection of models in the context of parsec-scale extragalactic jets will also be discussed.

scholarly journals Numerical simulation of dispersion of ammonia in industry space using the ANSYS

2018 ◽  
Vol 247 ◽  
pp. 00044
Author(s):  
Zdzisław Salamonowicz
Keyword(s):  
Numerical Simulations ◽  
Roughness Parameter ◽  
Numerical Approach ◽  
Chemical Equipment ◽  
Empirical Models ◽  
Average Roughness ◽  
Danger Zone ◽  
Industrial Installation ◽  
Heavy Gas ◽  
Selection Of

The article presents issues related to numerical simulations of the spread of dangerous substances in the air after emergency release from industrial installation. The work contains the results of numerical simulations of dispersion of ammonia and chlorine after emergency release made by using the ANSYS program, validated based on commonly used models: Gauss and heavy gas. Validation of experimental results based on research and empirical models allowed the selection of boundary parameters and the implementation of dispersion modelling in 3-d space taking into account technical infrastructure. Existing empirical models include terrain obstacles in the form of average roughness parameter, which is shown in general by the range of the danger zone without local topographic conditions. The numerical approach to modelling, in contrast to empirical models, allows to more accurately show the physicochemical phenomena occurring after release in 3-d space, both in the area around the chemical equipment and the buildings along the dangerous substance cloud.

Reflective Evolution Under Strategic Uncertainty

2019 ◽  
Vol 29 (02) ◽  
pp. 1950018 ◽  
Author(s):  
Arnaud Z. Dragicevic
Keyword(s):  
Population Dynamics ◽  
Numerical Simulations ◽  
Evolutionary Model ◽  
Competition Strategy ◽  
Strategic Uncertainty ◽  
Bifurcation Diagrams ◽  
Structured Population ◽  
To Come ◽  
The Impact ◽  
Negative Strategy

We consider population dynamics of agents who can both play the cooperative strategy and the competition strategy but ignore whether the game to come will be cooperative or noncooperative. For that purpose, we propose an evolutionary model, built upon replicator(–mutator) dynamics under strategic uncertainty, and study the impact of update decay. In replicator–mutator dynamics, we find that the strategy replication under certain mutation in an unstructured population is equivalent to a negative strategy replication in a structured population. Likewise, in replicator–mutator dynamics with decay, the strategy replication under certain mutation in a structured population is equivalent to a negative replication issued from an unstructured population. Our theoretical statements are supported by numerical simulations performed on bifurcation diagrams.

scholarly journals Scattering of Planetesimals from Young Planetary Disks: Application to the β Pictoris System

2002 ◽  
Vol 12 ◽  
pp. 225-228
Author(s):  
Hervé Beust ◽  
Philippe Thébault
Keyword(s):  
Numerical Simulations ◽  
Numerical Study ◽  
Mass Density ◽  
Mean Motion Resonances ◽  
Dynamical Characteristics ◽  
Mean Motion ◽  
Mass Estimate ◽  
Plausible Mechanism ◽  
Dynamical Origin

AbstractTransient redshifted events monitored in the spectrum ofβPictoris have been interpreted as resulting from the evaporation of numerous comet-like bodies in the vicinity of this star. The dynamical origin for this phenomenon is attributed to mean-motion resonances (4:1 and 3:1) with a Jovian-like planet. Numerical simulations of this phenomenon are able to correctly reproduce the dynamical characteristics of the star-grazers observed. The numerical study allows to estimate the density of the planetesimal disk from which the bodies are supposed to originate, i.e. ∼ a few 108bodies per AU. A key issue with this model is the refilling of the resonances, as without refilling they should be cleared within a few 105yr and the observed phenomenon should stop. Collisions among planetesimals are a plausible mechanism. Collisional simulations show that collisions are able to sustain the observed phenomenon over much more than 106yr, provided the population of the disk is high enough. The mass density of this population is estimated to a few tens of Earth masses per AU, which is only marginally realistic. However, the mass estimate is very poorly constrained.

Subharmonic and Chaotic Motions of a Hybrid Squeeze-Film Damper-Mounted Rigid Rotor With Active Control

2002 ◽  
Vol 124 (2) ◽  
pp. 198-208 ◽  
Author(s):  
Chieh-Li Chen ◽  
Her-Terng Yau ◽  
Yunhua Li
Keyword(s):  
Lyapunov Exponent ◽  
Active Control ◽  
Chaotic Motion ◽  
Numerical Results ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Maximum Lyapunov Exponent ◽  
Rigid Rotor ◽  
Squeeze Film Damper

The hybrid squeeze-film damper bearing with active control is proposed in this paper. The pressure distribution and the dynamics of a rigid rotor supported by such bearing are studied. A PD (proportional-plus-derivative) controller is used to stabilize the rotor-bearing system. Numerical results show that, due to the nonlinear factors of oil film force, the trajectory of the rotor demonstrates a complex dynamics with rotational speed ratio s. Poincare´ maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the rotor trajectory in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent and fractal dimension concepts are used to determine if the system is in a state of chaotic motion. Numerical results show that the maximum Lyapunov exponent of this system is positive and the dimension of the rotor trajectory is fractal at the nondimensional speed ratio s=3.0, which indicate that the rotor trajectory is chaotic under such operation condition. In order to avoid the nonsynchronous chaotic vibrations, an increased proportional gain is applied to control this system. It is shown that the rotor trajectory will leave chaotic motion to periodic motion in the steady state under control action.

scholarly journals Nonlinear Dynamic Analysis of Rotor Rub-Impact System

2019 ◽  
Vol 2019 ◽  
pp. 1-20
Author(s):  
Youfeng Zhu ◽  
Zibo Wang ◽  
Qiang Wang ◽  
Xinhua Liu ◽  
Hongyu Zang ◽  
...  
Keyword(s):  
Periodic Motion ◽  
Chaotic Motion ◽  
Nonlinear Dynamic Analysis ◽  
Period Doubling ◽  
Time History ◽  
Rotor System ◽  
Quasiperiodic Motion ◽  
Rotor Bearing ◽  
Motion Period ◽  
Bearing System

A dynamic model of a double-disk rub-impact rotor-bearing system with rubbing fault is established. The dynamic differential equation of the system is solved by combining the numerical integration method with MATLAB. And the influence of rotor speed, disc eccentricity, and stator stiffness on the response of the rotor-bearing system is analyzed. In the rotor system, the time history diagram, the axis locus diagram, the phase diagram, and the Poincaré section diagram in different rotational speeds are drawn. The characteristics of the periodic motion, quasiperiodic motion, and chaotic motion of the system in a given speed range are described in detail. The ways of the system entering and leaving chaos are revealed. The transformation and evolution process of the periodic motion, quasiperiodic motion, and chaotic motion are also analyzed. It shows that the rotor system enters chaos by the way of the period-doubling bifurcation. With the increase of the eccentricity, the quasi-periodicity evolution is chaotic. The quasiperiodic motion evolves into the periodic three motion phenomenon. And the increase of the stator stiffness will reduce the chaotic motion period.

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