Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System

2002 ◽  
pp. 156-158
Keyword(s):  
Dynamical System ◽  
Cutoff Frequency ◽  
First Order

scholarly journals BACH FLOWS OF PRODUCT MANIFOLDS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250039 ◽  
Author(s):  
SANJIT DAS ◽  
SAYAN KAR
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Ricci Flow ◽  
Flow Characteristics ◽  
Geometric Flow ◽  
Flow Equations ◽  
First Order ◽  
Bach Tensor ◽  
Point Condition ◽  
Future Work

We investigate various aspects of a geometric flow defined using the Bach tensor. First, using a well-known split of the Bach tensor components for (2, 2) unwarped product manifolds, we solve the Bach flow equations for typical examples of product manifolds like S2 × S2, R2 × S2. In addition, we obtain the fixed-point condition for general (2, 2) manifolds and solve it for a restricted case. Next, we consider warped manifolds. For Bach flows on a special class of asymmetrically warped 4-manifolds, we reduce the flow equations to a first-order dynamical system, which is solved exactly to find the flow characteristics. We compare our results for Bach flow with those for Ricci flow and discuss the differences qualitatively. Finally, we conclude by mentioning possible directions for future work.

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

scholarly journals On asymptotically stable sets

1970 ◽  
Vol 17 (2) ◽  
pp. 181-186 ◽  
Author(s):  
D. Desbrow
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Metric Space ◽  
Physical System ◽  
Asymptotically Stable ◽  
Stable Sets ◽  
Compact Closure ◽  
First Order ◽  
Closed Sets ◽  
The Future

In this paper we study closed sets having a neighbourhood with compact closure which are positively asymptotically stable under a flow on a metric space X. For an understanding of this and the rest of the introduction it is sufficient for the reader to have in mind as an example of a flow a system of first order, autonomous ordinary differential equations describing mathematically a time-independent physical system; in short a dynamical system. In a flow a set M is positively stable if the trajectories through all points sufficiently close to M remain in the future in a given neighbourhood of M. The set M is positively asymptotically stable if it is positively stable and, in addition, trajectories through all points of some neighbourhood of M approach M in the future.

scholarly journals Note on the Sensitivity of Simulated Solutions of the Nonlinear Singularly Perturbed Dynamical System on the Used Different Rewriting into a System of First Order Differential Equations

2016 ◽  
Vol 24 (39) ◽  
pp. 51-55
Author(s):  
Vladimír Liška ◽  
Zuzana Šútova ◽  
Dušan Pavliak
Keyword(s):  
Dynamical System ◽  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Numerical Scheme ◽  
Singularly Perturbed ◽  
First Order ◽  
First Order Differential Equations

Abstract In this paper we analyze the sensitivity of solutions to a nonlinear singularly perturbed dynamical system based on different rewriting into a System of the First Order Differential Equations to a numerical scheme. Numerical simulations of the solutions use numerical methods implemented in MATLAB.

scholarly journals Stability and Anti-Chaos Control of Discrete Quadratic Maps

2021 ◽  
pp. 1675-1685
Author(s):  
Sarbast H. Mikaee ◽  
George Maria Selvam ◽  
Vignesh D. Shanmugam ◽  
Bewar Beshay
Keyword(s):  
Dynamical System ◽  
Bifurcation Theory ◽  
Chaos Control ◽  
Order System ◽  
System Of Equations ◽  
Quadratic Maps ◽  
First Order ◽  
Current State ◽  
Chaotic Nature ◽  
Parameter Values

A dynamical system describes the consequence of the current state of an event or particle in future. The models expressed by functions in the dynamical systems are more often deterministic, but these functions might also be stochastic in some cases. The prediction of the system's behavior in future is studied with the analytical solution of the implicit relations (Differential, Difference equations) and simulations. A discrete-time first order system of equations with quadratic nonlinearity is considered for study in this work. Classical approach of stability analysis using Jury's condition is employed to analyze the system's stability. The chaotic nature of the dynamical system is illustrated by the bifurcation theory. The enhancement of chaos is performed using Cosine Chaotification Technique (CCT). Simulations are carried out for different parameter values.

scholarly journals Periodic Solutions for the Eccentricity and Inclination First Order Resonance

1992 ◽  
Vol 152 ◽  
pp. 231-232
Author(s):  
Marisa A. Nitto ◽  
Wagner Sessin
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Periodic Solutions ◽  
Reference System ◽  
Resonance Problem ◽  
Order Resonance ◽  
First Order ◽  
Primary Body ◽  
Different Types ◽  
The Subject

For the first order resonance, the problem of the motion of two small masses around a primary body can be of three different types: eccentricity, inclination or eccentricity-inclination. The eccentricity type resonance problem has been the subject of several works since Poincaré(1902). The inclination type resonance problem was studied by Greenberg(1973) who used a particular reference system to obtain an integrable auxiliary system. Sessin and Ferraz-Mello(1984) studied the eccentricity type resonance problem considering the eccentricities of the orbits of the two small masses. Sessin(1991) study the inclination type resonance problem for an arbitrary reference system. In this paper we will study a dynamical system that includes both types of resonance. This study is based in the models developed by Sessin and Ferraz-Mello(1984) and Sessin(1991). The resulting system of differential equation is non-integrable; thus, the families of trivial periodic solutions are studied.

Dynamic Properties of Small Chamber Air Gages

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Miroslaw Rucki ◽  
Czeslaw Janusz Jermak
Keyword(s):  
Dynamical System ◽  
Pressure Transducer ◽  
Dynamic Properties ◽  
Back Pressure ◽  
Step Response ◽  
Measuring Chamber ◽  
First Order ◽  
Circular Frequency ◽  
Dynamical Measurement ◽  
Industrial Measurement

In the paper, the investigations on the dynamic properties of air gauges are presented. As an important parameter, the time response underwent the analysis. The measurement of the amplitudes of back-pressure pk dependent on the input signal circular frequency ω for the group of air gauges with various parameters has been performed, too. The obtained results underwent comparative analysis with the results of investigation of the step response. The examinations of the step response of typical back-pressure air gage with small measuring chamber and with a piezoresistive pressure transducer led to the conclusion that its behavior is very close to the first-order dynamical system. The examined air gauges could be successfully exploited in the industrial measurement of values changing in time (dynamical measurement).

NONCOMMUTATIVE BELL POLYNOMIALS

1996 ◽  
Vol 06 (05) ◽  
pp. 635-644 ◽  
Author(s):  
RAINER SCHIMMING ◽  
SAAD ZAGLOUL RIDA
Keyword(s):  
Dynamical System ◽  
Differential Operator ◽  
Bell Polynomials ◽  
Exponential Integral ◽  
Recursive Definition ◽  
First Order ◽  
Taylor Coefficients ◽  
Order Matrix

The recursive definition for the sequence of the Bell polynomials is generalized to noncommutative variables and then explicitly solved. As applications, we present formulas for the powers of a first-order matrix-valued differential operator, of the “substantial derivative” to a dynamical system, and for the Taylor coefficients of the time-ordered exponential integral.

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