METRIC UNIVERSALITY OF ORDER IN ONE-DIMENSIONAL DYNAMICS

1993 ◽  
Vol 03 (03) ◽  
pp. 567-572
Author(s):  
MICHAEL FRAME ◽  
DAVID PEAK
Keyword(s):  
Dynamical System ◽  
Critical Point ◽  
Parameter Space ◽  
Nonlinear Dynamical System ◽  
Unimodal Maps ◽  
Nonlinear Dynamical ◽  
One Dimensional ◽  
Wide Range ◽  
Parameter Values ◽  
Universal Representation

The orbit of the critical point of a nonlinear dynamical system defines a family of functions in the parameter space of the system. For unimodal maps a renormalization makes these functions indistinguishable over a wide range of parameter values. The universal representation of these functions leads directly to a number of interesting results: (1) the positions in the parameter space of the windows of order; (2) the sizes of the windows of order; (3) measures of distortion in the window structure; and (4) various generalized Feigenbaum numbers. We explicitly discuss the examples of the quadratic and sine maps.

INTERACTIVE GRAPHICAL EXPLORATION OF MULTIDIMENSIONAL NONLINEAR DYNAMICAL SYSTEMS

1992 ◽  
Vol 02 (02) ◽  
pp. 251-261 ◽  
Author(s):  
JUDY CHALLINGER
Keyword(s):  
Dynamical System ◽  
Parameter Space ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Three Dimensional ◽  
Initial Point ◽  
Unit Cube ◽  
Dimensional Parameter ◽  
Data Set ◽  
Nonlinear Dynamical

This paper discusses the application of an inherently three-dimensional graphical representation tool, isosurfaces, as a means to interactively explore and visualize the attractors of a nonlinear dynamical system with a fifteen-dimensional parameter space. A program has been written which allows the scientist to interactively select and visualize three-dimensional sub-spaces of the fifteen-dimensional parameter space. The dynamical system used to illustrate these concepts is a discrete-time, nonlinear, three-nation Richardson model with economic constraints. This dynamical system, which models the shifting alliances of nations in an arms race, maps an initial point in the unit cube to another point in the unit cube after multiple iterations of the model functions. Using an isosurface function on the resulting volumetric data set, surfaces indicating the changing alliances of nations are generated and rendered.

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.

scholarly journals Multivalued Discrete Tomography Using Dynamical System That Describes Competition

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Takeshi Kojima ◽  
Tetsushi Ueta ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Theoretical Analysis ◽  
Continuous Time ◽  
Numerical Experiments ◽  
Nonlinear Dynamical System ◽  
Reconstructed Image ◽  
Optimization Approach ◽  
Discrete Tomography ◽  
Nonlinear Dynamical ◽  
Time Optimization

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown.

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