scholarly journals The study of chaotic and regular regimes of the fractal oscillators FitzHugh-Nagumo

2018 ◽  
Vol 62 ◽  
pp. 02017 ◽  
Author(s):  
Olga Lipko ◽  
Roman Parovik
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Nerve Impulse ◽  
Chaotic Attractors ◽  
Control Parameters ◽  
Schmidt Orthogonalization ◽  
Non Local ◽  
Explicit Finite Difference ◽  
Maximum Lyapunov Exponents ◽  
Orthogonalization Procedure

In this paper we study the conditions for the existence of chaotic and regular oscillatory regimes of the hereditary oscillator FitzHugh-Nagumo (FHN), a mathematical model for the propagation of a nerve impulse in a membrane. To achieve this goal, using the non-local explicit finite-difference scheme and Wolf’s algorithm with the Gram-Schmidt orthogonalization procedure and the spectra of the maximum Lyapunov exponents were also constructed depending on the values of the control parameters of the model of the FHN. The results of the calculations showed that there are spectra of maximum Lyapunov exponents both with positive values and with negative values. The results of the calculations were also confirmed with the help of oscillograms and phase trajectories, which indicates the possibility of the existence of both chaotic attractors and limit cycles.

scholarly journals Research dynamic modes of stick-slip effect with the account of hereditarity

2018 ◽  
Vol 62 ◽  
pp. 02015 ◽  
Author(s):  
Roman Parovik
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponents ◽  
Slip Effect ◽  
Stick Slip ◽  
Phase Trajectories ◽  
Wolff Algorithm ◽  
Schmidt Orthogonalization ◽  
Maximum Lyapunov Exponents

In study with the help of the spectrum of maximal Lyapunov exponents, dynamic regimes of the stick-slip effect were studied with allowance effect of hereditarity. Spectrum of the Lyapunov exponents were constructed using the Wolff algorithm with Gram-Schmidt orthogonalization depending on the values of the control parametersfriction and adhesion coefficients, as well as fractional index values, which determine the heredity of the dynamical system under consideration. The existence of an area of positive values of the maximum Lyapunov exponents is shown, which indicates the presence of chaotic regimes. Oscillograms and phase trajectories are constructed.

Thermal Analysis of Expressway Considering Wind Effect

2013 ◽  
Vol 419 ◽  
pp. 895-904
Author(s):  
X. Cao ◽  
H. Miyashita ◽  
T. Kako ◽  
Z. Zhang ◽  
B. Song
Keyword(s):  
Mathematical Model ◽  
Thermal Analysis ◽  
Thermal Conduction ◽  
Computer Calculation ◽  
Basic Mechanism ◽  
Weather Data ◽  
Wind Effect ◽  
Fortran Language ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

This paper reports a method of thermal analysis of expressway and the results of analysis of four expressways currently used in Japan. The authors built a mathematical model based on the principle of thermal conduction. For the boundary conditions in this mathematical model the influence of solar radiation, wind and air temperature etc. are taken into consideration. Explicit finite difference method is used in the analysis. The authors made an analysis program in Fortran language. Four main expressways distributing from the northern to the southern in Japan are chosen as the objects of this study. The observed weather data of the hottest days experienced by these expressways during the past 30 years is input into the computer calculation. The basic mechanism of expressway temperature change and effect factors are illuminated. The results are reported and discussed.

scholarly journals Метод расчета спектра показателей Ляпунова для систем с запаздыванием

2018 ◽  
Vol 44 (9) ◽  
pp. 19
Author(s):  
А.Д. Колоскова ◽  
О.И. Москаленко ◽  
А.А. Короновский
Keyword(s):  
Lyapunov Exponents ◽  
Delayed Feedback ◽  
Model Systems ◽  
Delay Systems ◽  
Control Parameters ◽  
Bifurcation Diagrams ◽  
Good Agreement

AbstractA method for calculating the spectrum of Lyapunov exponents for delay systems is proposed. To validate the method, a delayed-feedback oscillator and the Mackay–Glass equation are considered as model systems. For both systems, bifurcation diagrams and spectra of Lyapunov exponents are constructed as functions of one of the control parameters. The results are shown to be in good agreement with each other, which indicates the efficacy of the proposed method.

scholarly journals DYNAMIC SIMULATION AND COMPOSITION CONTROL IN A 10 L MIXING TANK

REAKTOR ◽  
2012 ◽  
Vol 14 (2) ◽  
pp. 95
Author(s):  
Yulius Deddy Hermawan ◽  
Gogot Haryono
Keyword(s):  
Mathematical Model ◽  
Dynamic Simulation ◽  
Closed Loop ◽  
Step Function ◽  
Open Loop ◽  
Liquid Volume ◽  
Control Parameters ◽  
Software Environment ◽  
Composition Control ◽  
Volumetric Rate

The open loop experiment of composition dynamic in a 10 L mixing tank has been successfully done inlaboratory. A 10 L tank was designed for mixing of water (as a stream-1) and salt solution (as astream-2 with salt concentration, c2 constant). An electric stirrer was employed to obtain uniformcomposition in tank. In order to keep the liquid volume constant, the system was designed overflow. Inthis work, 2 composition control configurations have been proposed; they are Alternative-1 andAlternative-2. For Alternative-1, the volumetric-rate of stream-1 was chosen as a manipulatedvariable, while the volumetric-rate of stream-2 was chosen as a manipulated variable for Alternative-2. The composition control parameters for both alternatives have been tuned experimentally. Thevolumetric-rate of manipulated variable was changed based on step function. The outlet stream’scomposition response (c3) to a change in the input volumetric-rate has been investigated. Thisexperiment gave Proportional Integral Derivative (PID) control parameters. The gain controllers Kc[cm6/(gr.sec)] for Alternative-1 and Alternative-2 are -34200 and 40459 respectively. Integral timeconstant ( tI) and Derivative time constant (tD) for both alternatives are the same, i.e. tI = 16 second,and tD = 4 second. Furthermore, closed loop dynamic simulation using computer programming wasalso done to evaluate the resulted tuning parameters. The developed mathematical model ofcomposition control system in a mixing tank was solved numerically. Such mathematical model wasrigorously examined in Scilab software environment. The results showed that closed loop responses inPID control were faster than those in P and PI controls.

scholarly journals SINGULAR ORBITS AND DYNAMICS AT INFINITY OF A CONJUGATE LORENZ-LIKE SYSTEM

2015 ◽  
Vol 20 (2) ◽  
pp. 148-167 ◽  
Author(s):  
Fengjie Geng ◽  
Xianyi Li
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Exponents ◽  
Heteroclinic Orbits ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Basic Properties ◽  
Homoclinic And Heteroclinic Orbits ◽  
Quadratic Nonlinearities ◽  
Singular Orbits

A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretical analysis. The forming mechanisms of compound structures of its new chaotic attractors obtained by merging together two simple attractors after performing one mirror operation are also presented. Furthermore, some of its other complex dynamical behaviours, which include the existence of singularly degenerate heteroclinic cycles, the existence of homoclinic and heteroclinic orbits and the dynamics at infinity, etc, are formulated in detail. In the meantime, some problems deserving further investigations are presented.

An On-Line Model to Calculate the Strip Temperature at Run-Out Table of Tisco’s Hot Strip Mill

2003 ◽  
Author(s):  
A. Mukhopadhyay ◽  
S. Sikdar ◽  
S. Sen
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Hot Strip Mill ◽  
Water Cooling ◽  
Coiling Temperature ◽  
Line Model ◽  
Finite Difference Technique ◽  
Hot Strip ◽  
On Line ◽  
Explicit Finite Difference

A Mathematical model has been developed to predict the temperature profile of the strip during water-cooling on the Run-out Table (ROT) of the Hot Strip Mill (HSM). This work describes the development and implementation of the model at Tisco’s HSM. The model has been developed using Explicit Finite Difference technique to predict the coiling temperature (CT). The model has been implemented successfully after having been validated with the actual coiling temperature (CT) for several thousand coils. A number of grades of steel with various thicknesses have been tested with this on-line model and the agreement of actual CT with the predicted ones was found very good. The on-line model is used to calculate the cooling rates at different segments of the strip that are used to obtain microstructure and mechanical properties.

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