Suppose we fix σ = 10 and β = 8/3 in the Lorenz system but leave ρ as a parameter.
(a) Show that there is only one equilibrium point for the system if ρ ≤ 1.
(b) Show that, if ρ >1, there are three equilibrium points and compute their locations.
(c) What can you conclude about the value ρ = 1?
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