Measures for the Characterization of Dynamic States of Dynamical Systems

2014 ◽  
Vol 64 (1) ◽  
pp. 1-7
Author(s):  
Youngtae KIM*
Keyword(s):  
Dynamical Systems ◽  
Dynamic States

A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS

1994 ◽  
Vol 04 (04) ◽  
pp. 979-998 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Chaotic Systems ◽  
Main Tool ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Unified Framework ◽  
Partial Synchronization ◽  
Chua’S Oscillator ◽  
And Control

In this paper, we give a framework for synchronization of dynamical systems which unifies many results in synchronization and control of dynamical systems, in particular chaotic systems. We define concepts such as asymptotical synchronization, partial synchronization and synchronization error bounds. We show how asymptotical synchronization is related to asymptotical stability. The main tool we use to prove asymptotical stability and synchronization is Lyapunov stability theory. We illustrate how many previous results on synchronization and control of chaotic systems can be derived from this framework. We will also give a characterization of robustness of synchronization and show that master-slave asymptotical synchronization in Chua’s oscillator is robust.

Numerical characterization of nonlinear dynamical systems using parallel computing: The role of GPUs approach

2016 ◽  
Vol 37 ◽  
pp. 143-162 ◽  
Author(s):  
Filipe I. Fazanaro ◽  
Diogo C. Soriano ◽  
Ricardo Suyama ◽  
Marconi K. Madrid ◽  
José Raimundo de Oliveira ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Numerical Characterization

scholarly journals Improving Entropy Estimates of Complex Network Topology for the Characterization of Coupling in Dynamical Systems

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 891 ◽  
Author(s):  
Teddy Craciunescu ◽  
Andrea Murari ◽  
Michela Gelfusa
Keyword(s):  
Dynamical Systems ◽  
Southern Oscillation ◽  
Geodesic Distance ◽  
Influenza Pandemic ◽  
Real Life ◽  
Coupled Model ◽  
Model Systems ◽  
Life Problems ◽  
Metric Distance

A new measure for the characterization of interconnected dynamical systems coupling is proposed. The method is based on the representation of time series as weighted cross-visibility networks. The weights are introduced as the metric distance between connected nodes. The structure of the networks, depending on the coupling strength, is quantified via the entropy of the weighted adjacency matrix. The method has been tested on several coupled model systems with different individual properties. The results show that the proposed measure is able to distinguish the degree of coupling of the studied dynamical systems. The original use of the geodesic distance on Gaussian manifolds as a metric distance, which is able to take into account the noise inherently superimposed on the experimental data, provides significantly better results in the calculation of the entropy, improving the reliability of the coupling estimates. The application to the interaction between the El Niño Southern Oscillation (ENSO) and the Indian Ocean Dipole and to the influence of ENSO on influenza pandemic occurrence illustrates the potential of the method for real-life problems.

Linear dynamic errors-in-variables models

1986 ◽  
Vol 23 (A) ◽  
pp. 23-39 ◽  
Author(s):  
M. Deistler
Keyword(s):  
Dynamical Systems ◽  
Transfer Functions ◽  
Errors In Variables ◽  
Linear Dynamical Systems ◽  
Linear Dynamic ◽  
Dynamic Errors ◽  
Non Gaussian ◽  
Inputs And Outputs

Linear dynamical systems where both inputs and outputs are contaminated by errors are considered. A characterization of the sets of all observationally equivalent transfer functions is given, the role of the causality assumption is investigated and conditions for identifiability in the case of Gaussian as well as non-Gaussian observations are derived.

scholarly journals The stability theorems for discrete dynamical systems on two-dimensional manifolds

1983 ◽  
Vol 90 ◽  
pp. 1-55 ◽  
Author(s):  
Atsuro Sannami
Keyword(s):  
Dynamical Systems ◽  
Smooth Manifold ◽  
Riemannian Metric ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Stability Theorems ◽  
The Stability

One of the basic problems in the theory of dynamical systems is the characterization of stable systems.Let M be a closed (i.e. compact without boundary) connected smooth manifold with a smooth Riemannian metric and Diffr (M) (r ≥ 1) denote the space of Cr diffeomorphisms on M with the uniform Cr topology.

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