I am currently studying chaos theory but am unsure what the difference is between the Lorenz system and the Lorenz attractor. Is the Lorenz attractor just the solution of the Lorenz system with $\beta=8/3,\sigma=10,\rho=28$? Or does the name 'Lorenz attractor' apply to more general parameter values?
2026-03-29 02:29:13.1774751353
When is the Lorenz system the Lorenz attractor?
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The attractor is a set of points in $\Bbb{R}^3$. You can see the definition of an attractor here: wikipedia. A quick summary is: For the parameter values you've given, solutions are attracted to the set -- if you imagine time going to infinity, then the solutions get closer and closer to the attractor.
The system is the set of equations itself.