Fault diagnosis in nonlinear dynamical systems based on left invertibility condition: A real-time application to three-tank system

2011 ◽  
Author(s):  
Juan L. Mata-Machuca ◽  
Rafael Martinez-Guerra ◽  
Jose J. Rincon-Pasaye
Keyword(s):  
Fault Diagnosis ◽  
Dynamical Systems ◽  
Real Time ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Left Invertibility ◽  
Tank System ◽  
Real Time Application

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.

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.

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