scholarly journals A Method of Symmetrization of Asymmetric Dynamical Systems

2005 ◽  
Vol 12 (4) ◽  
pp. 309-315 ◽  
Author(s):  
C.Q. Liu
Keyword(s):  
Dynamical Systems ◽  
Numerical Calculations ◽  
Equivalence Transformation ◽  
Symmetric Matrices ◽  
New Approach ◽  
Symmetric Systems

This paper presents an approach to transform asymmetric systems into symmetric systems by equivalence transformation and discusses what forms of restrictions should be imposed on the system matrices so that they can be simultaneously transformed into symmetric matrices. Conditions of symmetrizability obtained here are more “liberal” and numerical calculations of this transformation are more straightforward. Several examples are provided to illustrate the new approach.

On Symmetrizable Systems of Second Kind

2000 ◽  
Vol 67 (4) ◽  
pp. 797-802 ◽  
Author(s):  
S. Adhikari
Keyword(s):  
Structural Dynamics ◽  
Original Work ◽  
Similarity Transformation ◽  
Equivalence Transformation ◽  
Linear Transformations ◽  
Equivalence Transformations ◽  
Linear Dynamical Systems ◽  
New Approach ◽  
Multiple Parameter ◽  
Symmetric Systems

We discuss under what conditions multiple-parameter asymmetric linear dynamical systems can be transformed into equivalent symmetric systems by nonsingular linear transformations. So far, in structural dynamics literature this problem has been addressed in the context of the original work by Taussky. Taussky’s approach of symmetrization was based on similarity transformation. In this paper an approach is proposed to transform asymmetric systems into symmetric systems by equivalence transformation. We call Taussky’s approach of symmetrization by similarity transformation “first kind” and proposed approach by equivalence transformation “second kind.” Since equivalence transformations are most general nonsingular linear transformations, conditions of symmetrizability obtained here are more “liberal” than the first kind and numerical calculations also become more straightforward. Several examples are provided to illustrate the new approach. [S0021-8936(00)00504-3]

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

FREQUENCY SYNCHRONIZATION IN NETWORKS OF COUPLED OSCILLATORS, A MONOTONE DYNAMICAL SYSTEMS APPROACH

2009 ◽  
Vol 19 (12) ◽  
pp. 4107-4116 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Systems Approach ◽  
System Size ◽  
Coupling Scheme ◽  
Frequency Synchronization ◽  
Nonlinear Coupling ◽  
New Approach ◽  
Monotone Dynamical Systems

We propose a new approach to investigate the frequency synchronization in networks of coupled oscillators. By making use of the theory of monotone dynamical systems, we show that frequency synchronization occurs in networks of coupled oscillators, provided the coupling scheme is symmetric, connected, and strongly cooperative. Our criterion is independent of the system size, the coupling strength and the details of the connections, and applies also to nonlinear coupling schemes.

scholarly journals Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory

Atmosphere ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 248
Author(s):  
Nan Chen ◽  
Xiao Hou ◽  
Qin Li ◽  
Yingda Li
Keyword(s):  
Information Theory ◽  
Dynamical Systems ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Model Error ◽  
High Dimensions ◽  
New Approach ◽  
Fluctuation Dissipation ◽  
Spectrum Density ◽  
Non Gaussian

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Quantifying the model error and model uncertainty plays an important role in understanding and predicting complex dynamical systems. In the first part of this article, a simple information criterion is developed to assess the model error in imperfect models. This effective information criterion takes into account the information in both the equilibrium statistics and the temporal autocorrelation function, where the latter is written in the form of the spectrum density that permits the quantification via information theory. This information criterion facilitates the study of model reduction, stochastic parameterizations, and intermittent events. In the second part of this article, a new efficient method is developed to improve the computation of the linear response via the Fluctuation Dissipation Theorem (FDT). This new approach makes use of a Gaussian Mixture (GM) to describe the unperturbed probability density function in high dimensions and avoids utilizing Gaussian approximations in computing the statistical response, as is widely used in the quasi-Gaussian (qG) FDT. Testing examples show that this GM FDT outperforms qG FDT in various strong non-Gaussian regimes.

MODELING LINEAR DYNAMICAL SYSTEMS BY CONTINUOUS-VALUED CELLULAR AUTOMATA

2007 ◽  
Vol 18 (05) ◽  
pp. 833-848 ◽  
Author(s):  
JUAN CARLOS SECK TUOH MORA ◽  
MANUEL GONZALEZ HERNANDEZ ◽  
NORBERTO HERNANDEZ ROMERO ◽  
AARON RODRIGUEZ TREJO ◽  
SERGIO V. CHAPA VERGARA
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Linear Systems ◽  
Configuration Space ◽  
Integration Method ◽  
Numerical Calculations ◽  
Linear Dynamical Systems ◽  
Original Part

This paper exposes a procedure for modeling and solving linear systems using continuous-valued cellular automata. The original part of this work consists on showing how the cells in the automaton may contain both real values and operators for carrying out numerical calculations and solve a desired problem. In this sense the automaton acts as a program, where data and operators are mixed in the evolution space for obtaining the correct calculations. As an example, Euler's integration method is implemented in the configuration space in order to achieve an approximated solution for a dynamical system. Three examples showing linear behaviors are presented.

scholarly journals DIFFERENTIAL GEOMETRY AND MECHANICS: APPLICATIONS TO CHAOTIC DYNAMICAL SYSTEMS

2006 ◽  
Vol 16 (04) ◽  
pp. 887-910 ◽  
Author(s):  
JEAN-MARC GINOUX ◽  
BRUNO ROSSETTO
Keyword(s):  
Differential Geometry ◽  
Dynamical Systems ◽  
Slow Manifold ◽  
Van Der Pol ◽  
New Approach ◽  
Metric Properties ◽  
Chaotic Dynamical Systems ◽  
Mechanics Concepts ◽  
The One ◽  
Curvature And Torsion

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical expression of the slow manifold equation of slow-fast autonomous dynamical systems starting from kinematics variables (velocity, acceleration and over-acceleration or jerk). The attractivity of the slow manifold will be characterized thanks to a criterion proposed by Henri Poincaré. Moreover, the specific use of acceleration will make it possible on the one hand to define slow and fast domains of the phase space and on the other hand, to provide an analytical equation of the slow manifold towards which all the trajectories converge. The attractive slow manifold constitutes a part of these dynamical systems attractor. So, in order to propose a description of the geometrical structure of attractor, a new manifold called singular manifold will be introduced. Various applications of this new approach to the models of Van der Pol, cubic-Chua, Lorenz, and Volterra–Gause are proposed.

A New Approach to the Theory of Canonical Decomposition of Linear Dynamical Systems

1973 ◽  
Vol 11 (1) ◽  
pp. 148-158 ◽  
Author(s):  
P. D’Alessandro ◽  
A. Isidori ◽  
A. Ruberti
Keyword(s):  
Dynamical Systems ◽  
Canonical Decomposition ◽  
Linear Dynamical Systems ◽  
New Approach

A New Approach to the Control Design of Fuzzy Dynamical Systems

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ye-Hwa Chen
Keyword(s):  
Dynamical Systems ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Control Design ◽  
Form Solution ◽  
Bottom Line ◽  
New Approach ◽  
Fuzzy Dynamical System ◽  
The Cost ◽  
Fuzzy Dynamical Systems

A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

Sign in / Sign up

Export Citation Format

Share Document