Computer Methods for Study of Fractal Properties of Systems with Chaotic Dynamics

1999 ◽  
Vol 31 (4-5) ◽  
pp. 12-21
Author(s):  
Mikhail V. Artyushenko ◽  
Oleg V. Nikitenko
Keyword(s):  
Chaotic Dynamics ◽  
Computer Methods ◽  
Fractal Properties

FRACTAL TRACER PATTERNS IN OPEN HYDRODYNAMICAL FLOWS: THE CASE OF LEAPFROGGING VORTEX PAIRS

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 33-53
Author(s):  
Á. PÉNTEK ◽  
T. TÉL ◽  
Z. TOROCZKAI
Keyword(s):  
Velocity Field ◽  
Chaotic Dynamics ◽  
Initial Conditions ◽  
Vortex Pairs ◽  
Tracer Particles ◽  
Fractal Properties ◽  
Fractal Patterns ◽  
Passive Tracers ◽  
Time Periodic ◽  
Chaotic Saddle

Patterns obtained by using tracer particles to visualize open hydrodynamical flows are investigated. As an example, the advection problem of passive tracers in the time-periodic velocity field of leapfrogging vortex pairs is considered. We show that the patterns are fractal if the tracer dynamics is chaotic, i.e., there exists a chaotic saddle, and if the initial conditions overlap with the stable manifold of this chaotic set (that is itself a fractal). Dye particles not advected away very quickly then accumulate on the unstable manifold of the chaotic saddle and the fractal dimension of such patterns is thus independent of the initial conditions. The time evolution of the fractal patterns appearing on snaphsots is followed within one period of the velocity field. We investigate which features of the chaotic dynamics determine the fractal properties. They turn out to be independent of when the snapshots are taken. The entropy function of the local Lyapunov exponents is computed based on the scattering motion of the tracer particles, along with the f(α) spectrum of the chaotic saddle.

Chaotic Dynamics

1996 ◽  
Author(s):  
Gregory L. Baker ◽  
Jerry P. Gollub
Keyword(s):  
Chaotic Dynamics

Forecasting and Estimating SETAR Models under the Influence of Chaotic Dynamics

2012 ◽  
Author(s):  
Ricardo Gimeno ◽  
Ruth Mateos de Cabo ◽  
Lorenzo Escot ◽  
Pilar Grau ◽  
Elena Olmedo
Keyword(s):  
Chaotic Dynamics

Fractal properties of neurophysiologic signals in rat somatosensory cortex

2005 ◽  
Vol 25 (1_suppl) ◽  
pp. S186-S186
Author(s):  
Peter Herman ◽  
Shaun A Wahab ◽  
Andras Eke ◽  
Fahmeed Hyder
Keyword(s):  
Somatosensory Cortex ◽  
Fractal Properties ◽  
Rat Somatosensory Cortex
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