Perturbative analysis of quasiperiodic route to chaos in the circle map

1990 ◽  
Vol 42 (1) ◽  
pp. 19-21 ◽  
Author(s):  
K M Valsamma ◽  
G Ambika ◽  
K Babu Joseph
Keyword(s):  
Circle Map ◽  
Quasiperiodic Route To Chaos ◽  
Route To Chaos

Routes to Chaos in Neural Networks with Random Weights

1998 ◽  
Vol 08 (07) ◽  
pp. 1463-1478 ◽  
Author(s):  
D. J. Albers ◽  
J. C. Sprott ◽  
W. D. Dechert
Keyword(s):  
Dynamical System ◽  
Neural Networks ◽  
Function Space ◽  
Dynamic Properties ◽  
Monte Carlo Study ◽  
Random Dynamical System ◽  
Network Function ◽  
The Neural Network ◽  
Quasiperiodic Route To Chaos ◽  
Route To Chaos

Neural networks are dense in the space of dynamical system. We present a Monte Carlo study of the dynamic properties along the route to chaos over random dynamical system function space by randomly sampling the neural network function space. Our results show that as the dimension of the system (the number of dynamical variables) is increased, the probability of chaos approaches unity. We present theoretical and numerical results which show that as the dimension is increased, the quasiperiodic route to chaos is the dominant route. We also qualitatively analyze the dynamics along the route.

Universality in the quasiperiodic route to chaos

1996 ◽  
Vol 6 (1) ◽  
pp. 32-42 ◽  
Author(s):  
T. W. Dixon ◽  
T. Gherghetta ◽  
B. G. Kenny
Keyword(s):  
Quasiperiodic Route To Chaos ◽  
Route To Chaos
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