A Dynamical Systems Perspective on Music

1997 ◽  
Vol 15 (4) ◽  
pp. 529-545
Author(s):  
David Burrows
Keyword(s):  
Dynamical Systems ◽  
Systems Perspective

Correlations Between Hysteretic Categorical and Continuous Judgments of Perceptual Stimuli Supporting a Unified Dynamical Systems Approach to Perception

Perception ◽  
2017 ◽  
Vol 47 (1) ◽  
pp. 44-66 ◽  
Author(s):  
S. Kim ◽  
T. D. Frank
Keyword(s):  
Dynamical Systems ◽  
Systems Approach ◽  
Brain Activity ◽  
Equation Model ◽  
Measurement Scale ◽  
Systems Perspective ◽  
Within Subjects ◽  
Scale Measure ◽  
Positive Correlations ◽  
Experimental Findings

We report from two variants of a figure-ground experiment that is known in the literature to involve a bistable perceptual domain. The first variant was conducted as a two-alternative forced-choice experiment and in doing so tested participants on a categorical measurement scale. The second variant involved a Likert scale measure that was considered to represent a continuous measurement scale. The two variants were conducted as a single within-subjects experiment. Measures of bistability operationalized in terms of hysteresis size scores showed significant positive correlations across the two response conditions. The experimental findings are consistent with a dualistic interpretation of self-organizing perceptual systems when they are described on a macrolevel by means of so-called amplitude equations. This is explicitly demonstrated for a Lotka–Volterra–Haken amplitude equation model of task-related brain activity. As a by-product, the proposed dynamical systems perspective also sheds new light on the anchoring problem of producing numerical, continuous judgments.

scholarly journals A random dynamical systems perspective on stochastic resonance

Nonlinearity ◽  
2017 ◽  
Vol 30 (7) ◽  
pp. 2835-2853 ◽  
Author(s):  
Anna Maria Cherubini ◽  
Jeroen S W Lamb ◽  
Martin Rasmussen ◽  
Yuzuru Sato
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Random Dynamical Systems ◽  
Systems Perspective

COVID-19 ORDER PARAMETERS AND ORDER PARAMETER TIME CONSTANTS OF ITALY AND CHINA: A MODELING APPROACH BASED ON SYNERGETICS

2020 ◽  
Vol 28 (03) ◽  
pp. 589-608 ◽  
Author(s):  
T. D. FRANK
Keyword(s):  
Dynamical Systems ◽  
Compartment Model ◽  
Order Parameters ◽  
Unstable State ◽  
Human Populations ◽  
Time Constants ◽  
Systems Perspective ◽  
Infection Dynamics ◽  
Model Spaces ◽  
Systems Framework

From a dynamical systems perspective, COVID-19 infectious disease emerges via an instability in human populations. Accordingly, the human population free of COVID-19 infected individuals is an unstable state and the dynamics away from that unstable state is a bifurcation. Recent research has determined COVID-19 relevant bifurcation parameters for various countries in terms of basic reproduction ratios. However, little is known about the relevant order parameters (synergetics) of COVID-19 bifurcations and the corresponding time constants. Those order parameters describe directions in compartment model spaces in which infection dynamics initially evolves. The corresponding time constants describe the speed of the dynamics along those directions. COVID-19 order parameters and their time constants are derived within a standard SEIR dynamical systems framework and determined explicitly for two published studies on COVID-19 trajectories in Italy and China. The results suggest the existence of certain relationships between order parameters, time constants, and reproduction ratios. However, the examples from Italy and China also suggest that COVID-19 order parameters and time constants in general depend on regional differences and the stage of the local COVID-19 epidemic under consideration. These findings may help to improve the forecasting of COVID-19 outbreaks in new hotspots around the world.

The dynamics of language

1999 ◽  
Vol 22 (2) ◽  
pp. 284-285
Author(s):  
Peter W. Culicover ◽  
Andrzej Nowak
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Simple Model ◽  
Syntactic Structure ◽  
Neural Assemblies ◽  
Systems Perspective ◽  
Model Based ◽  
Associative Structures

To deal with syntactic structure, one needs to go beyond a simple model based on associative structures, and to adopt a dynamical systems perspective, where each phrase and sentence of a language is represented as a trajectory in a syntactic phase space. Neural assemblies could possibly be used to produce dynamics that in principle could handle syntax along these lines.

Sign in / Sign up

Export Citation Format

Share Document