scholarly journals Modeling of information channel by using of pseudorandom signals of nonlinear dynamical system

2020 ◽  
Vol 22 (4) ◽  
pp. 79-87
Author(s):  
I. K. Nasyrov ◽  
V. V. Andreev
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Detection Algorithm ◽  
Main Step ◽  
Operating Characteristics ◽  
Nonlinear Dynamical ◽  
Pseudorandom Signals ◽  
Chaotic Signals ◽  
Correlation Properties

Pseudorandom signals of nonlinear dynamical systems are studied and the possibility of their application in information systems analyzed. Continuous and discrete dynamical systems are considered: Lorenz System, Bernoulli and Henon maps. Since the parameters of dynamical systems (DS) are included in the equations linearly, the principal possibility of the state linear control of a nonlinear DS is shown. The correlation properties comparative analysis of these DSs signals is carried out.. Analysis of correlation characteristics has shown that the use of chaotic signals in communication and radar systems can significantly increase their resolution over the range and taking into account the specific properties of chaotic signals, it allows them to be hidden. The representation of nonlinear dynamical systems equations in the form of stochastic differential equations allowed us to obtain an expression for the likelihood functional, with the help of which many problems of optimal signal reception are solved. It is shown that the main step in processing the received message, which provides the maximum likelihood functionals, is to calculate the correlation integrals between the components and the systems under consideration. This made it possible to base the detection algorithm on the correlation reception between signal components. A correlation detection receiver was synthesized and the operating characteristics of the receiver were found.

A New Method for Equilibria and Stability Analysis of Nonlinear Dynamical Systems

2014 ◽  
Vol 534 ◽  
pp. 131-136
Author(s):  
Long Cao ◽  
Yi Hua Cao
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
Vehicle Model ◽  
Nonlinear Dynamical ◽  
Novel Method ◽  
Linearized System ◽  
Continuation Algorithm

A novel method based on numerical continuation algorithm for equilibria and stability analysis of nonlinear dynamical system is introduced and applied to an aircraft vehicle model. Dynamical systems are usually modeled with differential equations, while their equilibria and stability analysis are pure algebraic problems. The newly-proposed method in this paper provides a way to solve the equilibrium equation and the eigenvalues of the locally linearized system simultaneously, which avoids QR iterations and can save much time.

scholarly journals Lagrange and practical stability criteria for dynamical systems with nonlinear perturbations

2012 ◽  
Vol 22 (1) ◽  
pp. 43-58
Author(s):  
Assen Krumov
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Computer Control ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Nonlinear Operators ◽  
Nonlinear Dynamical

Lagrange and practical stability criteria for dynamical systems with nonlinear perturbationsIn the paper two classes of nonlinear dynamical system with perturbations are considered. The sufficient conditions for robust Lagrange and practical stability are proven with theorems, applying the theory of nonlinear operators of the functional analysis. The presented criteria give also the bounds of the analyzed dynamical processes. Three examples comparing the numerical computer solutions and the analytical investigation of the stability of the systems are given. The method can be applied to analytical and computer modeling of nonlinear dynamical systems, synthesis of computer control and optimization.

scholarly journals Active Control Of Oscillation Patterns In Nonlinear Dynamical Systems And Their Mathematical Modelling

2014 ◽  
Vol 22 (341) ◽  
pp. 29-33
Author(s):  
Zuzana Šutová ◽  
Róbert Vrábeľ
Keyword(s):  
Dynamical Systems ◽  
Singular Perturbation ◽  
Active Control ◽  
Nonlinear Dynamical Systems ◽  
Frequency Control ◽  
Nonlinear Dynamical System ◽  
Perturbation Parameter ◽  
Singular Perturbation Theory ◽  
Frequency Change ◽  
Nonlinear Dynamical

Abstract The article deals with the active control of oscillation patterns in nonlinear dynamical systems and its possible use. The purpose of the research is to prove the possibility of oscillations frequency control based on a change of value of singular perturbation parameter placed into a mathematical model of a nonlinear dynamical system at the highest derivative. This parameter is in singular perturbation theory often called small parameter, as ε → 0+. Oscillation frequency change caused by a different value of the parameter is verified by modelling the system in MATLAB.

scholarly journals STABILITY AND STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS

2017 ◽  
Vol 20 (1) ◽  
pp. 61-70
Author(s):  
P. Sattayatham ◽  
R. Saelim ◽  
S. Sujitjorn
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Feedback Controllers ◽  
Nonlinear Dynamical ◽  
System A ◽  
Continuous Feedback ◽  
Stability And Stabilization ◽  
The Stability

Exponential and asymptotic stability for a class of nonlinear dynamical systems with uncertainties is investigated.  Based on the stability of the nominal system, a class of bounded continuous feedback controllers is constructed.  By such a class of controllers, the results guarantee exponential and asymptotic stability of uncertain nonlinear dynamical system.  A numerical example is also given to demonstrate the use of the main result.

NONLINEAR DYNAMICAL SYSTEM AND CHAOS SYNCHRONIZATION

2008 ◽  
Vol 18 (05) ◽  
pp. 1531-1537 ◽  
Author(s):  
AYUB KHAN ◽  
PREMPAL SINGH
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Chaos Synchronization ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Numerical Techniques ◽  
Nonlinear Dynamical ◽  
Chaotic Dynamical Systems ◽  
Response System ◽  
Identical Response

Chaos synchronization of nonlinear dynamical systems has been studied through theoretical and numerical techniques. For the synchronization of two identical nonlinear chaotic dynamical systems a theorem has been constructed based on the Lyapunov function, which requires a minimal knowledge of system's structure to synchronize with an identical response system. Numerical illustrations have been provided to verify the theorem.

Optimal tracking control of nonlinear dynamical systems

2008 ◽  
Vol 464 (2097) ◽  
pp. 2341-2363 ◽  
Author(s):  
Firdaus E Udwadia
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Weighted Norm ◽  
Analytical Dynamics ◽  
Control Cost ◽  
Nonlinear Dynamical ◽  
First Order ◽  
Time Optimal

This paper presents a simple methodology for obtaining the entire set of continuous controllers that cause a nonlinear dynamical system to exactly track a given trajectory. The trajectory is provided as a set of algebraic and/or differential equations that may or may not be explicitly dependent on time. Closed-form results are also provided for the real-time optimal control of such systems when the control cost to be minimized is any given weighted norm of the control, and the minimization is done not just of the integral of this norm over a span of time but also at each instant of time. The method provided is inspired by results from analytical dynamics and the close connection between nonlinear control and analytical dynamics is explored. The paper progressively moves from mechanical systems that are described by the second-order differential equations of Newton and/or Lagrange to the first-order equations of Poincaré, and then on to general first-order nonlinear dynamical systems. A numerical example illustrates the methodology.

IMPROVED PARAMETER ESTIMATION FROM NOISY TIME SERIES FOR NONLINEAR DYNAMICAL SYSTEMS

2007 ◽  
Vol 17 (05) ◽  
pp. 1741-1752 ◽  
Author(s):  
TOMOMICHI NAKAMURA ◽  
YOSHITO HIRATA ◽  
KEVIN JUDD ◽  
DEVIN KILMINSTER ◽  
MICHAEL SMALL
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Dynamical Systems ◽  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Parameter Estimates ◽  
Nonlinear Dynamical ◽  
Observational Noise

In this paper we consider the problem of estimating the parameters of a nonlinear dynamical system given a finite time series of observations that are contaminated by observational noise. The least squares method is a standard method for parameter estimation, but for nonlinear dynamical systems it is well known that the least squares method can result in biased estimates, especially when the noise is significant relative to the nonlinearity. In this paper, it is demonstrated that by combining nonlinear noise reduction and least squares parameter fitting it is possible to obtain more accurate parameter estimates.

On Periodic Motions in the First-Order Nonlinear Systems

2016 ◽  
Author(s):  
Albert C. J. Luo ◽  
Yeyin Xu ◽  
Zhaobo Chen
Keyword(s):  
Dynamical System ◽  
Fourier Series ◽  
Dynamical Systems ◽  
Analytical Solutions ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Nonlinear Dynamical System ◽  
Periodic Motions ◽  
Nonlinear Dynamical ◽  
First Order

In this paper, analytical solutions of periodic motions in the first-order nonlinear dynamical system are discussed from the finite Fourier series expression. The first-order nonlinear dynamical system is transformed to the dynamical system of coefficients in the Fourier series. From investigation of such dynamical system of coefficients, the analytical solutions of periodic motions are obtained, and the corresponding stability and bifurcation of periodic motions will be determined. In fact, this method provides a frequency-response analysis of periodic motions in nonlinear dynamical systems, which is alike the Laplace transformation of periodic motions for nonlinear dynamical systems. The harmonic frequency-amplitude curves are obtained for different-order harmonic terms in the Fourier series. Through such frequency-amplitude curves, the nonlinear characteristics of periodic motions in the first-order nonlinear system can be determined. From analytical solutions, the initial conditions are obtained for numerical simulations. From such initial conditions, numerical simulations are completed in comparison of the analytical solutions of periodic motions.

Approximation of the Frequency-Energy Dependence in the Nonlinear Dynamical Systems

2016 ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Duffing Oscillator ◽  
Nonlinear Dynamical System ◽  
Nonlinear Energy Sink ◽  
High Energy ◽  
Initial Energy ◽  
Nonlinear Dynamical ◽  
High Energy Level

In this work, a method is introduced for extracting the approximate backbone branches of the frequency-energy plot from the numerical simulation response of the nonlinear dynamical system. The duffing oscillator is firstly considered to describe the method and later a linear oscillator (LO) coupled with a nonlinear energy sink (NES) is also considered for further demonstration. The systems of concern are numerically simulated at an arbitrary high level of initial input energy. Accordingly, the obtained responses of these systems are employed via the proposed method to extract an approximation for the fundamental backbone branches of the frequency-energy plot. The obtained backbones have been found in excellent agreement with the exact backbones of the considered systems. Even though these approximate backbones have been obtained for only one high energy level, they are still valid for any other initial energy below that level. In addition, they are not affected by the damping variations in the considered systems. Unlike other existing methods, the proposed approach is applicable to well-approximate the backbone branches of the large-scale nonlinear dynamical systems.

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