TRUMPET AND TRUMPET PLAYER: A HIGHLY NONLINEAR INTERACTION STUDIED IN THE FRAMEWORK OF NONLINEAR DYNAMICS

2001 ◽  
Vol 11 (07) ◽  
pp. 1801-1814
Author(s):  
CHRISTOPHE VERGEZ ◽  
XAVIER RODET
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Real Time ◽  
Physical Model ◽  
Nonlinear Interaction ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
General Behavior ◽  
Highly Nonlinear

For musical purposes, a real-time physical model of trumpet-like instruments was built. The model exhibits different behaviors which are studied in the framework of nonlinear dynamical systems. Periodic, quasi-periodic, chaotic and intermittency regimes are identified and studied in order to better understand the general behavior of the model, which is essential for musical use.

A Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept

1982 ◽  
Vol 49 (4) ◽  
pp. 895-902 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Nonlinear Dynamical Systems ◽  
Global Analysis ◽  
Cell Structure ◽  
The State ◽  
Probabilistic Theory ◽  
Nonlinear Dynamical ◽  
Linear Ordinary Differential Equations ◽  
Highly Nonlinear

Developed in the paper is a probabilistic theory for nonlinear dynamical systems. The theory is based on discretizing the state space into a cell structure and using the cell probability functions to describe the state of a system. Although the dynamical system may be highly nonlinear the probabilistic formulation always leads to a set of linear ordinary differential equations. The evolution of the probability distribution among the cells can then be studied by applying the theory of Markov processes to this set of equations. It is believed that this development possibly offers a new approach to the global analysis of nonlinear systems.

Periodicity and Nonlinearity of Nonlinear Dynamical Systems Under Periodic Excitation

2009 ◽  
Author(s):  
Lu Han ◽  
Liming Dai ◽  
Huayong Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamical Systems ◽  
Research Work ◽  
Nonlinear Dynamic Systems ◽  
Periodic Excitation ◽  
Nonlinear Dynamical

Periodicity and nonlinearity of nonlinear dynamic systems subjected to regular external excitations are studied in this research work. Diagnoses of regular and chaotic responses of nonlinear dynamic systems are performed with the implementation of a newly developed Periodicity Ratio in combining with the application of Lyapunov Exponent. The properties of the nonlinear dynamics systems are classified into four categories: periodic, irregular-nonchaotic, quasiperiodic and chaotic, each corresponding to their Periodicity Ratios. Detailed descriptions about diagnosing the responses of the four categories are presented with utilization of the Periodicity Ratio.

Experimental verification of horseshoes from electronic circuits

1995 ◽  
Vol 353 (1701) ◽  
pp. 59-64 ◽  
Keyword(s):  
Dynamical Systems ◽  
Real Time ◽  
Experimental Verification ◽  
Electronic Circuit ◽  
Nonlinear Dynamical Systems ◽  
Electronic Circuits ◽  
Poincaré Maps ◽  
Nonlinear Dynamical ◽  
Poincare Maps ◽  
Return Maps

Poincaré maps are an important tool in analysing the behaviour of nonlinear dynamical systems. If the system to be investigated is an electronic circuit or can be modelled by an electronic circuit, these maps can be visualized on an oscilloscope thereby facilitating real-time investigations. In this paper, sequences of return maps eventually leading to horseshoes are described. These maps are experimentally taken both from non-autonomous and autonomous circuits.

A phase transition between localist and distributed representation

2000 ◽  
Vol 23 (4) ◽  
pp. 486-486
Author(s):  
Peter C. M. Molenaar ◽  
Maartje E. J. Raijmakers
Keyword(s):  
Phase Transition ◽  
Dynamical Systems ◽  
Real Time ◽  
Bifurcation Analysis ◽  
Nonlinear Dynamical Systems ◽  
Continuous Variation ◽  
Distributed Representation ◽  
Distributed Representations ◽  
Nonlinear Dynamical

Bifurcation analysis of a real-time implementation of an ART network, which is functionally similar to the generalized localist model discussed in Page's manifesto shows that it yields a phase transition from local to distributed representation owing to continuous variation of the range of inhibitory connections. Hence there appears to be a qualitative dichotomy between local and distributed representations at the level of connectionistic networks conceived of as instances of nonlinear dynamical systems.

scholarly journals Nonlinear dynamics in psychology

2001 ◽  
Vol 6 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Stephen J. Guastello
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Cognitive Science ◽  
Systems Theory ◽  
Professional Practice ◽  
Nonlinear Dynamical Systems ◽  
Empirical Studies ◽  
Psychological Theory ◽  
Nonlinear Dynamical ◽  
Psychological Science

This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.

scholarly journals Physics-informed Spline Learning for Nonlinear Dynamics Discovery

2021 ◽  
Author(s):  
Fangzheng Sun ◽  
Yang Liu ◽  
Hao Sun
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Differential Equations ◽  
Climate Science ◽  
Analytical Form ◽  
Optimization Strategy ◽  
Governing Equations ◽  
Nonlinear Dynamical ◽  
High Level

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate science, engineering and social science. To address this fundamental challenge, we propose a novel Physics-informed Spline Learning (PiSL) framework to discover parsimonious governing equations for nonlinear dynamics, based on sparsely sampled noisy data. The key concept is to (1) leverage splines to interpolate locally the dynamics, perform analytical differentiation and build the library of candidate terms, (2) employ sparse representation of the governing equations, and (3) use the physics residual in turn to inform the spline learning. The synergy between splines and discovered underlying physics leads to the robust capacity of dealing with high-level data scarcity and noise. A hybrid sparsity-promoting alternating direction optimization strategy is developed for systematically pruning the sparse coefficients that form the structure and explicit expression of the governing equations. The efficacy and superiority of the proposed method have been demonstrated by multiple well-known nonlinear dynamical systems, in comparison with two state-of-the-art methods.

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