A Dynamical Systems Approach to Musical Tonality

2010 ◽  
pp. 193-211 ◽  
Author(s):  
Edward W. Large
Keyword(s):  
Dynamical Systems ◽  
Systems Approach

Streamer saturation: a dynamical systems approach

2006 ◽  
Vol 351 (6) ◽  
pp. 417-423 ◽  
Author(s):  
F. Jenko
Keyword(s):  
Dynamical Systems ◽  
Systems Approach

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.

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.

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