Visualizing nonlinear vector field topology

1998 ◽  
Vol 4 (2) ◽  
pp. 109-116 ◽  
Author(s):  
G. Scheuermann ◽  
H. Kruger ◽  
M. Menzel ◽  
A.P. Rockwood
Keyword(s):  
Vector Field ◽  
Vector Field Topology ◽  
Nonlinear Vector

Implicit Visualization of 2D Vector Field Topology for Periodic Orbit Detection

2021 ◽  
pp. 159-180
Author(s):  
Alexander Straub ◽  
Grzegorz K. Karch ◽  
Filip Sadlo ◽  
Thomas Ertl
Keyword(s):  
Vector Field ◽  
Periodic Orbit ◽  
Vector Field Topology

Fast Combinatorial Vector Field Topology

2011 ◽  
Vol 17 (10) ◽  
pp. 1433-1443 ◽  
Author(s):  
Jan Reininghaus ◽  
Christian Lowen ◽  
Ingrid Hotz
Keyword(s):  
Vector Field ◽  
Vector Field Topology ◽  
Combinatorial Vector Field

Representation and display of vector field topology in fluid flow data sets

Computer ◽  
1989 ◽  
Vol 22 (8) ◽  
pp. 27-36 ◽  
Author(s):  
J. Helman ◽  
L. Hesselink
Keyword(s):  
Fluid Flow ◽  
Vector Field ◽  
Data Sets ◽  
Flow Data ◽  
Vector Field Topology

An Observer Approach for Deterministic Learning Using Patchy Neural Networks with Applications to Fuzzy Cognitive Networks

2011 ◽  
Vol 2 (1) ◽  
pp. 1-16 ◽  
Author(s):  
H. E. Psillakis ◽  
M. A. Christodoulou ◽  
T. Giotis ◽  
Y. Boutalis
Keyword(s):  
Neural Networks ◽  
Vector Field ◽  
Error Term ◽  
Duffing Oscillator ◽  
Cognitive Networks ◽  
Deterministic Learning ◽  
Simulation Results ◽  
Persistency Of Excitation ◽  
Nonlinear Vector ◽  
Excitation Conditions

In this paper, a new methodology is proposed for deterministic learning with neural networks. Using an observer that employs the integral of the sign of the error term, asymptotic estimation of the respective nonlinear vector field is achieved. Patchy Neural Networks (PNNs) are introduced to identify the unknown nonlinearity from the observer’s output and the state measurements. The proposed scheme achieves learning with a single pass from the respective patches and does not need standard persistency of excitation conditions. Furthermore, the PNN weights are updated algebraically, reducing the computational load of learning significantly. Simulation results for a Duffing oscillator and a fuzzy cognitive network illustrate the effectiveness of the proposed approach.

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