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.

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 Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov

2021 ◽  
Vol 254 ◽  
pp. 02014
Author(s):  
Roman Parovik ◽  
Zafar Rakhmonov ◽  
Rakhim Zunnunov
Keyword(s):  
Fractional Derivative ◽  
Dynamic System ◽  
Lyapunov Exponents ◽  
Fractional Derivatives ◽  
Chaotic Regime ◽  
Research Tool ◽  
Phase Trajectories ◽  
Fractional Dynamic System ◽  
Maximum Lyapunov Exponents

The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benettin-Wolf algorithm. It is shown that the existence of chaotic regimes is possible. In particular, the spectrum of the maximum Lyapunov exponents of the order of the fractional derivative contains positive values, which indicates the presence of a chaotic regime. Phase trajectories were also constructed to confirm these results. It was also confirmed that the orders of fractional derivatives are responsible for dissipation in the system under consideration.

Two Simplest Quadratic Chaotic Maps Without Equilibrium

2018 ◽  
Vol 28 (12) ◽  
pp. 1850144 ◽  
Author(s):  
Shirin Panahi ◽  
Julien C. Sprott ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic Maps ◽  
Basin Of Attraction ◽  
Hidden Attractor ◽  
Return Map ◽  
Right Hand ◽  
Dynamical Properties ◽  
The Right

Two simple chaotic maps without equilibria are proposed in this paper. All nonlinearities are quadratic and the functions of the right-hand side of the equations are continuous. The procedure of their design is explained and their dynamical properties such as return map, bifurcation diagram, Lyapunov exponents, and basin of attraction are investigated. These maps belong to the hidden attractor category which is a newly introduced category of dynamical system.

scholarly journals Application of the dynamic Lorentz model to modeling the motion of a rigid body

2021 ◽  
pp. 32-36
Author(s):  
Nikolay Makeyev ◽  
Keyword(s):  
Dynamical System ◽  
Qualitative Research ◽  
Rigid Body ◽  
Body Motion ◽  
Dynamic Equations ◽  
Lorentz Model ◽  
Dissipative Forces ◽  
System Parameters ◽  
Phase Trajectories ◽  
Inertia Forces

A qualitative research of the field of phase trajectories of the system of dynamic equations of an absolutely rigid body was carried out, moving around the selected pole under the influence of gyroscopic, dissipative forces and Coriolis inertia forces. The equations of body motion are reduced to a dynamical system generating a Lorentz attractor. Under parametric constraints imposed on the equations of a dynamical system, the structure of its phase trajectories is described depending on the values of the system parameters.

Simulacija i odstranjivanje stick-slip efekta servosistema sprovodnog aparata hidraulične turbine

2021 ◽  
Vol 23 (1) ◽  
pp. 37-41
Author(s):  
Darko Babunski ◽  
◽  
Emil Zaev ◽  
Atanasko Tuneski ◽  
Laze Trajkovski ◽  
...  
Keyword(s):  
Hydraulic Cylinder ◽  
Friction Model ◽  
Slip Effect ◽  
Hydraulic Systems ◽  
Hydraulic Actuator ◽  
Stick Slip ◽  
Hydro Turbine ◽  
Servo Mechanism ◽  
The Mathematical Model ◽  
Slip Phenomenon

Friction is a repeatable and undesirable problem in hydraulic systems where always has to be a tendency for its removal. In this paper, the friction model is presented through which the most accurate results are achieved and the way of friction compensation, approached trough technique presented with the mathematical model of a hydraulic cylinder of a hydro turbine wicket gate controlled by a servomechanism. Mathematical modelling of a servo mechanism and hydraulic actuator, and also the simulation of hydraulic cylinder as a part of a hydro turbine wicket gate hydraulic system where the stick-slip phenomenon is present between the system components that are in contact is presented. Applied results in this paper and the theory behind them precisely demonstrate under what circumstances the stick-slip phenomenon appears in such a system. The stick-slip effect is simulated using Simulink and Hopsan software and the analysis of the results are given in this paper. Removal of the stick-slip effect is presented with the design of a cascade control implemented to control the behaviour of the system and remove the appearance of a jerking motion.

A Novel Trans-Scale Precision Positioning Stage Based on the Stick-Slip Effect

2012 ◽  
Vol 2 (2) ◽  
pp. 1-14 ◽  
Author(s):  
Bowen Zhong ◽  
Liguo Chen ◽  
Zhenhua Wang ◽  
Lining Sun
Keyword(s):  
Friction Model ◽  
Slip Effect ◽  
Precision Positioning ◽  
Stick Slip ◽  
Kinematics Model ◽  
Lugre Friction Model ◽  
Positioning Stage ◽  
Simulation Results ◽  
Relationship Of ◽  
The Relationship

This article focuses on developing a novel trans-scale precision positioning stage based on the stick-slip effect. The stick-slip effect is introduced and the rigid kinematics model of the stick-slip driving is established. The forward and return displacement equations of each step of the stick-slip driving are deduced. The relationship of return displacement and the acceleration produced by friction are obtained according to displacement equations. Combining with LuGre friction model, the flexible dynamics model of the stick-slip driving is established and simulated by using Simulink software. Simulation results show that the backward displacement will reduce with the acceleration of the slider produced by dynamic friction force, the rigid kinematics model is also verified by simulation results which are explained in further detail in the article.

scholarly journals Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Bo. Yan ◽  
Punam K. Prasad ◽  
Sayan Mukherjee ◽  
Asit Saha ◽  
Santo Banerjee
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponents ◽  
Alpha Particles ◽  
Coexisting Attractors ◽  
Plasma System ◽  
Electrostatic Waves ◽  
Lunar Wake ◽  
Dynamical Complexity ◽  
Suprathermal Electrons ◽  
Different Types

Dynamical complexity and multistability of electrostatic waves are investigated in a four-component homogeneous and magnetized lunar wake plasma constituting of beam electrons, heavier ions (alpha particles, He++), protons, and suprathermal electrons. The unperturbed dynamical system of the considered lunar wake plasma supports nonlinear and supernonlinear trajectories which correspond to nonlinear and supernonlinear electrostatic waves. On the contrary, the perturbed dynamical system of lunar wake plasma shows different types of coexisting attractors including periodic, quasiperiodic, and chaotic, investigated by phase plots and Lyapunov exponents. To confirm chaotic and nonchaotic dynamics in the perturbed lunar wake plasma, 0−1 chaos test is performed. Furthermore, a weighted recurrence-based entropy is implemented to investigate the dynamical complexity of the system. Numerical results show existence of chaos with variation of complexity in the perturbed dynamics.

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