Computation of Lyapunov Characteristic Exponents Using Parallel Computing

2017 ◽  
Author(s):  
Hubertus F. von Bremen ◽  
Michael J. Bonilla
Keyword(s):  
Dynamical System ◽  
Parallel Implementation ◽  
Symmetric Matrix ◽  
Computer Memory ◽  
Characteristic Exponents ◽  
Lyapunov Characteristic Exponents ◽  
Computationally Expensive ◽  
Simulation Results ◽  
Arbitrary Dimensions ◽  
Derivatives Of

In [1] a method to accurately compute the Lyapunov Characteristic Exponents of continuous dynamical systems of arbitrary dimensions was presented. However, it can be computationally expensive, because it requires the computation of the time derivatives of the entries of the exponential of a skew-symmetric matrix. In this paper, we present an implementation of the method in [1] that takes advantage of the fact that some of the computations can be done in parallel. The speedup in the computations depends on the number of CPU cores used and the computer memory. Numerical simulations show improvements in efficiency when using the parallel implementation. Our implementation retains the accuracy of the method in [1] with the added advantage of a speedup in computations. Numerical simulation results are presented for a dynamical system of dimension seven and one of dimension forty-nine.

scholarly journals An Improved Chaotic Detection System for Metal Detectors

2021 ◽  
Vol 2087 (1) ◽  
pp. 012065
Author(s):  
Wenjing Hu
Keyword(s):  
Detection System ◽  
Duffing Oscillator ◽  
Threshold Value ◽  
Matlab Simulation ◽  
Metal Detector ◽  
Duffing System ◽  
Characteristic Exponents ◽  
Lyapunov Characteristic Exponents ◽  
Simulation Results ◽  
Metal Detectors

Abstract This paper first applies a chaotic system-Duffing oscillator to a metal detector, and uses RHR algorithm to compute two Lyapunov characteristics exponents of the Duffing system. In this way, the two Lyapunov characteristic exponents can help to judge the Duffing system being chaotic or not quantitatively. And also help to get the threshold value more accurately. Then a simulation model of Duffing system fit for detectors is established by Matlab. Simulation results indicate that an suitable Duffing system can improve the sensitivity of a detector effectively.

Simulation and Analysis of Dynamic Characteristics of Rolling Motion of Rotational Molding Ship

2014 ◽  
Vol 556-562 ◽  
pp. 1278-1281
Author(s):  
Qi Guo Yao ◽  
Yu Liang Liu
Keyword(s):  
Parametric Resonance ◽  
Factorization Method ◽  
Operating Conditions ◽  
Qr Factorization ◽  
Rolling Motion ◽  
Rotational Molding ◽  
Longitudinal Waves ◽  
Characteristic Exponents ◽  
Lyapunov Characteristic Exponents ◽  
Simulation Results

Parametric resonance can lead to roll motions and endanger the ship, cargo and crew. The QR-factorization method for calculating lyapunov characteristic exponents (LCEs) was introduced. And then, parametric resonance stability of ships in longitudinal waves was analyzed by taking the fishing-entertainment rotational molding boat as an example. Simulation results show that, this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.

scholarly journals Distributed Control and the Lyapunov Characteristic Exponents in the Model of Infectious Diseases

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
M. Bershadsky ◽  
M. Chirkov ◽  
A. Domoshnitsky ◽  
S. Rusakov ◽  
I. Volinsky
Keyword(s):  
Infectious Diseases ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Distributed Control ◽  
Stationary Point ◽  
Treatment Time ◽  
Simulation Models ◽  
Characteristic Exponents ◽  
Data Comparison ◽  
Lyapunov Characteristic Exponents

The Marchuk model of infectious diseases is considered. Distributed control to make convergence to stationary point faster is proposed. Medically, this means that treatment time can be essentially reduced. Decreasing the concentration of antigen, this control facilitates the patient’s condition and gives a certain new idea of treating the disease. Our approach involves the analysis of integro-differential equations. The idea of reducing the system of integro-differential equations to a system of ordinary differential equations is used. The final results are given in the form of simple inequalities on the parameters. The results of numerical calculations of simulation models and data comparison in the case of using distributive control and in its absence are given.

scholarly journals On the flat spacetime Galileons and the Born–Infeld type structures

2015 ◽  
Vol 24 (06) ◽  
pp. 1550041
Author(s):  
Cuauhtemoc Campuzano ◽  
Rubén Cordero ◽  
Miguel Cruz ◽  
Efraín Rojas
Keyword(s):  
Scalar Field ◽  
Variational Analysis ◽  
Momentum Density ◽  
Type Structure ◽  
Field Theories ◽  
Flat Spacetime ◽  
Arbitrary Dimensions ◽  
Derivatives Of ◽  
Galileon Field

We show how the flat spacetime Galileon field theories (FSGFT) in arbitrary dimensions can be obtained through a Born–Infeld (BI) type structure. This construction involves a brane metric and nonlinear combinations of derivatives of a scalar field. Our setup gives rise to some Galileon tensors and vectors useful for the variational analysis which are related to the momentum density of the probe Lovelock branes floating in a N-dimensional flat bulk. We find further that the Noether currents associated to these Galileon theories may be written in terms of such tensors.

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