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Visual physics and mathematics/Chua system
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File:A long Chua line.gif
The Chua system is a system of three ordinary differential equations (Differential equations, dynamical systems and an introduction to chaos, Hirsch, Morris William., Smale, Stephen, Devaney, Robert Luke, 2004):
dx/dt = a(y - x3/16 + x/6)
dy/dt = x - y + z
dz/dt = -by
For example b=28 and a =15.4
It is a deterministic three-dimensional flow:
File:A flow on a Chua line.gif
All trajectories converge towards an attractor:
File:A very long Chua line 2.gif
It is a strange attractor because it is chaotic. A moving point circulates on the 8 in a way that seems disordered: a few turns on the left part of the 8 then a few turns on the right part and so on, but the number of turns on each part is unpredictable.
A zoom on the Chua attractor:
File:Zoom on a Chua line.gif
The attractor varies depending on the parameter a:
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