NOISY CHAOS IN A QUASI-INTEGRABLE HAMILTONIAN SYSTEM WITH TWO DOF UNDER HARMONIC AND BOUNDED NOISE EXCITATIONS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250117 ◽  
Author(s):  
C. B. GAN ◽  
Y. H. WANG ◽  
S. X. YANG ◽  
H. LEI
Keyword(s):  
Hamiltonian System ◽  
Integrable Hamiltonian System ◽  
Melnikov Method ◽  
Threshold Region ◽  
Mean Square ◽  
Bounded Noise ◽  
Onset Of Chaos ◽  
Extended Approach ◽  
The Mean ◽  
Quasi Integrable Hamiltonian System

This paper presents an extended form of the high-dimensional Melnikov method for stochastically quasi-integrable Hamiltonian systems. A quasi-integrable Hamiltonian system with two degree-of-freedom (DOF) is employed to illustrate this extended approach, from which the stochastic Melnikov process is derived in detail when the harmonic and the bounded noise excitations are imposed on the system, and the mean-square criterion on the onset of chaos is then presented. It is shown that the threshold of the onset of chaos can be adjusted by changing the deterministic intensity of bounded noise, and one can find the range of the parameter related to the bandwidth of the bounded noise excitation where the chaotic motion can arise more readily by investigating the changes of the threshold region. Furthermore, some parameters are chosen to simulate the sample responses of the system according to the mean-square criterion from the extended stochastic Melnikov method, and the largest Lyapunov exponents are then calculated to identify these sample responses.

On the Diffusion Along Resonant Lines in Continuous and Discrete Dynamical Systems

2003 ◽  
Vol 17 (22n24) ◽  
pp. 3964-3976
Author(s):  
Claude Froeschlé ◽  
Elena Lega
Keyword(s):  
Dynamical Systems ◽  
Hamiltonian System ◽  
Coupling Parameter ◽  
A Priori ◽  
Integrable Hamiltonian System ◽  
Discrete Dynamical Systems ◽  
Nekhoroshev Theorem ◽  
Symplectic Map ◽  
Quasi Integrable Hamiltonian System

We detect and measure diffusion along resonances in a discrete symplectic map for different values of the coupling parameter. Qualitatively and quantitatively the results are very similar to those obtained for a quasi-integrable Hamiltonian system, i.e. in agreement with Nekhoroshev predictions, although the discrete mapping does not fulfill completely, a priori, the conditions of the Nekhoroshev theorem.

HOMOCLINIC BIFURCATION AND CHAOS IN COUPLED SIMPLE PENDULUM AND HARMONIC OSCILLATOR UNDER BOUNDED NOISE EXCITATION

2005 ◽  
Vol 15 (01) ◽  
pp. 233-243 ◽  
Author(s):  
W. Q. ZHU ◽  
Z. H. LIU
Keyword(s):  
Harmonic Oscillator ◽  
Random Motion ◽  
Homoclinic Bifurcation ◽  
Mean Square ◽  
Bounded Noise ◽  
Bifurcation And Chaos ◽  
Simple Pendulum ◽  
Onset Of Chaos ◽  
Weakly Coupled ◽  
Threshold Amplitude

The homoclinic bifurcation and chaos in a system of weakly coupled simple pendulum and harmonic oscillator subject to light dampings and weakly external and (or) parametric excitation of bounded noise is studied. The random Melnikov process is derived and mean-square criteria is used to determine the threshold amplitude of the bounded noise for the onset of chaos in the system. The threshold amplitude is also determined by vanishing the numerically calculated maximal Lyapunov exponent. The threshold amplitudes are further confirmed by using the Poincaré maps, which indicate the path from periodic motion to chaos or from random motion to random chaos in the system as the amplitude of bounded noise increases.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals Electrical stimulator with mechanomyography-based real-time monitoring, muscle fatigue detection, and safety shut-off: a pilot study

2020 ◽  
Vol 65 (4) ◽  
pp. 461-468
Author(s):  
Jannatul Naeem ◽  
Nur Azah Hamzaid ◽  
Amelia Wong Azman ◽  
Manfred Bijak
Keyword(s):  
Muscle Fatigue ◽  
Real Time ◽  
Isometric Force ◽  
Mean Square ◽  
Clear Indication ◽  
Initial Value ◽  
Cord Injury ◽  
The Mean ◽  
Electrical Stimulator ◽  
Fatigue Detection

AbstractFunctional electrical stimulation (FES) has been used to produce force-related activities on the paralyzed muscle among spinal cord injury (SCI) individuals. Early muscle fatigue is an issue in all FES applications. If not properly monitored, overstimulation can occur, which can lead to muscle damage. A real-time mechanomyography (MMG)-based FES system was implemented on the quadriceps muscles of three individuals with SCI to generate an isometric force on both legs. Three threshold drop levels of MMG-root mean square (MMG-RMS) feature (thr50, thr60, and thr70; representing 50%, 60%, and 70% drop from initial MMG-RMS values, respectively) were used to terminate the stimulation session. The mean stimulation time increased when the MMG-RMS drop threshold increased (thr50: 22.7 s, thr60: 25.7 s, and thr70: 27.3 s), indicating longer sessions when lower performance drop was allowed. Moreover, at thr70, the torque dropped below 50% from the initial value in 14 trials, more than at thr50 and thr60. This is a clear indication of muscle fatigue detection using the MMG-RMS value. The stimulation time at thr70 was significantly longer (p = 0.013) than that at thr50. The results demonstrated that a real-time MMG-based FES monitoring system has the potential to prevent the onset of critical muscle fatigue in individuals with SCI in prolonged FES sessions.

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