scholarly journals An Approximate Technique of the State Estimation for Nonlinear Dynamical Systems under State-Dependent Observation Noise

1973 ◽  
Vol 9 (1) ◽  
pp. 91-99 ◽  
Author(s):  
Yoshifumi SUNAHARA ◽  
Akira OHSUMI ◽  
Hiroyuki KIKUI
Keyword(s):  
Dynamical Systems ◽  
State Estimation ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
State Dependent ◽  
Observation Noise ◽  
Dependent Observation

scholarly journals Phase Synchronization Is the Amplified Result by the Hilbert Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Hilbert Transform ◽  
Phase Synchronization ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
Large Correlation ◽  
Current Usage ◽  
The Hilbert Transform

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.

A Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept

1982 ◽  
Vol 49 (4) ◽  
pp. 895-902 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Nonlinear Dynamical Systems ◽  
Global Analysis ◽  
Cell Structure ◽  
The State ◽  
Probabilistic Theory ◽  
Nonlinear Dynamical ◽  
Linear Ordinary Differential Equations ◽  
Highly Nonlinear

Developed in the paper is a probabilistic theory for nonlinear dynamical systems. The theory is based on discretizing the state space into a cell structure and using the cell probability functions to describe the state of a system. Although the dynamical system may be highly nonlinear the probabilistic formulation always leads to a set of linear ordinary differential equations. The evolution of the probability distribution among the cells can then be studied by applying the theory of Markov processes to this set of equations. It is believed that this development possibly offers a new approach to the global analysis of nonlinear systems.

Journal Bearing Identification Under Operating Conditions

1984 ◽  
Vol 106 (2) ◽  
pp. 178-182 ◽  
Author(s):  
Roger Stanway
Keyword(s):  
Dynamical Systems ◽  
State Estimation ◽  
Numerical Experiments ◽  
Journal Bearing ◽  
Basic Problem ◽  
Nonlinear Dynamical Systems ◽  
Operating Conditions ◽  
Nonlinear Dynamical ◽  
Using Data ◽  
Bearing Dynamics

This note describes an approach to the problem of identifying linearized journal bearing dynamics using data acquired under normal operating conditions. The basic problem is reformulated so that an existing algorithm for state estimation in noisy nonlinear dynamical systems can be applied. The results of some numerical experiments are presented to demonstrate the feasibility of the approach.

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