The Lorenz system is a nonlinear and deterministic system of three ordinary differential equations with three parameters which is widely used as simplified models for different biological, physical, chemical and electrical systems:
dx/dt = a(y-x);
dy/dt = x(b-z);
dz/dt = xy-cz;
for b1 the system has three fixed points, the structural fixed points.
When a=10 and c=8/3, at b=28, the system becomes chaotic with so many fixed points, much much greater than the original three. In fact, for the parameter values when the system is chaotic, in addition to the three mentioned fixed points of the system, a large number of fixed points appear. We name them, “the functional fixed points”.
1. what is the role of the three structural fixed points of the system in the formation of the strange attractor? 2. How do these fixed points appear? 3. How can these behavioral (functional) fixed points analytically be derived from the system’s equations? 4. How do these fixed points form the strange attractor of the system?
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