Adjoint operator method and normal forms of higher order for nonlinear dynamical system

1997 ◽  
Vol 18 (5) ◽  
pp. 449-461 ◽  
Author(s):  
Zhang Wei ◽  
Chen Yushu
Keyword(s):  
Dynamical System ◽  
Normal Forms ◽  
Adjoint Operator ◽  
Nonlinear Dynamical System ◽  
Operator Method ◽  
Higher Order ◽  
Nonlinear Dynamical

Improved Adjoint Operator Method and Normal Form of Nonlinear Dynamical System

2013 ◽  
Vol 437 ◽  
pp. 70-75
Author(s):  
Jun Jun Li ◽  
Xiao Qing Liu ◽  
Shi Zhu Yang
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Normal Form ◽  
Polynomial Solution ◽  
Adjoint Operator ◽  
Nonlinear Dynamical System ◽  
Solution Space ◽  
Partial Differential ◽  
Nonlinear Dynamical

An improved adjoint operator based on the adjoint operator concept of linear operator and S-N decomposition is proposed to calculate the normal forms of k order general nonlinear dynamic systems.Firstly, the whole polynomial solution space of homogeneous nilpotent partial differential equation are obtained.Secondly, the polynomial solution mentioned above is introduced into homogeneous semi-simple partial differential equation to find the whole polynomial solution space of a homogeneous linear partial differential equation Therefore, more polynomial first integrals need not be found and the simplest normal form of nonlinear dynamical system can be obtained easily. The example shows that the method is very effective.

scholarly journals RESONANT NORMAL FORMS AS CONSTRAINED LINEAR SYSTEMS

2002 ◽  
Vol 17 (10) ◽  
pp. 583-597 ◽  
Author(s):  
GIUSEPPE GAETA
Keyword(s):  
Dynamical System ◽  
Normal Form ◽  
Linear System ◽  
Normal Forms ◽  
Integration Method ◽  
Linear Part ◽  
Nonlinear Dynamical System ◽  
Nonlinear Dynamical ◽  
Finite Dimensional ◽  
Constrained Linear Systems

We show that a nonlinear dynamical system in Poincaré–Dulac normal form (in ℝn) can be seen as a constrained linear system; the constraints are given by the resonance conditions satisfied by the spectrum of (the linear part of) the system and identify a naturally invariant manifold for the flow of the "parent" linear system. The parent system is finite dimensional if the spectrum satisfies only a finite number of resonance conditions, as implied e.g. by the Poincaré condition. In this case our result can be used to integrate resonant normal forms, and sheds light on the geometry behind the classical integration method of Horn, Lyapounov and Dulac.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

DYNAMICAL ESTIMATION OF CALENDAR EFFECTS

2006 ◽  
Vol 06 (01) ◽  
pp. L7-L15
Author(s):  
ALEXANDROS LEONTITSIS
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Noise Level ◽  
Nonlinear Dynamical System ◽  
Main Tool ◽  
Experimental Results ◽  
Accurate Estimation ◽  
Nonlinear Dynamical ◽  
Correlation Integral ◽  
Calendar Effects

The paper introduces a method for estimation and reduction of calendar effects from time series, which their fluctuations are governed by a nonlinear dynamical system and additive normal noise. Calendar effects can be considered deviations of the distribution(s) of particular group(s) of observations that have a common characteristic related to the calendar. The concept of this method is the following: since the calendar effects are not related to the dynamics of the time series, the accurate estimation and reduction will result a time series with a smaller amount of noise level (i.e. more accurate dynamics). The main tool of this method is the correlation integral, due to its inherit capability of modeling both the dynamics and the additive normal noise. Experimental results are presented on the Nasdaq Cmp. index.

Sign in / Sign up

Export Citation Format

Share Document