scholarly journals An approximate method for analysing non-linear systems subject to random excitation

2000 ◽  
Vol 22 (1) ◽  
pp. 1-10
Author(s):  
Nguyen Dong Anh ◽  
Ninh Quang Hai
Keyword(s):  
Linear System ◽  
Random Excitation ◽  
Solution Technique ◽  
Moment Equations ◽  
Closed Set ◽  
White Noise Excitation ◽  
Non Linear ◽  
Linearized System ◽  
Non Linear Systems ◽  
Non Linear System

A solution technique based on the representation of the response of the non-linear system by a polynomial of the response of the linearized system is presented. The relation between the original non-linear system and the linearized system is introduced by considering the so-called extended moment equations and their closed set is to be solved to determine unknowns. For the Vanderpol oscillator subject to white noise excitation, the technique gives good approximation to the response moments as well as the probability density function.

Correlation Techniques for the Identification of Non-Linear Systems

1972 ◽  
Vol 5 (8) ◽  
pp. 316-321 ◽  
Author(s):  
R. J. Simpson ◽  
H. M. Power
Keyword(s):  
Linear System ◽  
Frequency Domain ◽  
Recent Work ◽  
Cross Correlation ◽  
Volterra Series ◽  
Kernel Functions ◽  
Non Linear ◽  
Non Linear Systems ◽  
Correlation Techniques ◽  
Non Linear System

The Volterra series expansion of the response of a non-linear system is described, along with its counterpart in the frequency domain. Cross-correlation methods for identifying the kernel functions which occur in this expansion are reviewed, with particular emphasis on techniques for obtaining the linear approximant to a non-linear system. Some recent work which appears to be unrelated to the Volterra approach is also discussed.

scholarly journals Identification of a Non-Linear System Using Volterra Series Model with Calculated Kernels by Legendre Orthogonal Function

2017 ◽  
Vol 6 (3) ◽  
pp. 185
Author(s):  
Vahid Mossadegh ◽  
Mahmood Ghanbari
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Volterra Series ◽  
Legendre Function ◽  
Model Parameters ◽  
Orthogonal Functions ◽  
Orthogonal Function ◽  
Non Linear ◽  
Non Linear Systems ◽  
Non Linear System

Modeling and identification of non-linear systems have gained lots of attentions especially in industrial processes. Most of the actual systems have non-linear behavior and the first and simplest solution in modeling such systems is to linearize them which in most cases the result of linearization is not satisfactory. In this paper, modeling of non-linear systems is investigated using Volterra series model based on Legendre orthogonal function. Expansion of Volterra series kernels by Legendre orthogonal functions causes a reduction in the number of model parameters; hence, complexity of calculations would be decreased. Besides, if the free parameter is selected properly in these orthogonal functions, error is reduced and convergence speed of parameters is increased which leads to an increase in identification accuracy. In this paper, identification of non-linear system is presented with Volterra series expanded by Legendre function and PSO algorithm is used to calculate the optimum free parameters of Legendre function. Finally, in order to validate the efficacy and accuracy, the proposed algorithm is implemented on a non-linear system i.e. heat exchanger with actual data

Coexistent of Solutions in Non-Linear Systems with Impacts

2014 ◽  
Vol 543-547 ◽  
pp. 1840-1843
Author(s):  
Jin Qian Feng ◽  
Yue Tang Rong ◽  
Jun Li Liu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Shooting Method ◽  
Duffing System ◽  
Coexistence Of Attractors ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Non Linear System

This paper proposes a corrected shooting method for a general non-linear system with impacts. We define the global Poincaré mapping for period orbits by the discontinuous mapping. It is suitable to construct the strategy of shooting method. As an illustrated example, we investigate the stability of period orbits in a Duffing system with impacts. In Addition, coexistence of attractors and bifurcations for period orbits are considered.

scholarly journals A STUDY ABOUT STABILITY OF TWO AND THREE SPECIES POPULATION MODELS

2020 ◽  
pp. 4-12
Author(s):  
REZAUL KARIM ◽  
MOHAMMAD ASIF AREFIN ◽  
AMINA TAHSIN ◽  
MD. ABDUS SATTAR
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Third Order ◽  
Characteristic Roots ◽  
Non Linear ◽  
Species Population ◽  
Non Linear Systems ◽  
The Stability ◽  
Non Linear System ◽  
Homogeneous Linear

In this article, we have discussed the stability of second order linear and non-linear systems by characteristic roots. In the case of non-linear system, we linearize the nonlinear system under certain specified conditions and study the stability of critical points of the linearized systems. Necessary theories have been presented, applied, and illustrated with examples. A self-contained theory for a homogeneous linear system of third order is built by using the basic concept of the differential equation.

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