Visual physics and mathematics/Chua system



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): For example b=28 and a =15.4
 * dx/dt = a(y - x3/16 + x/6)
 * dy/dt = x - y + z
 * dz/dt = -by

It is a deterministic three-dimensional flow:



All trajectories converge towards an attractor:



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:



The attractor varies depending on the parameter a: