Consider the famous Lorenz system:

x' = 10(y-x)

y’ = x(R-z)-y

z’ = xy-8/3*z

What is in there when R = 28, which is not in there when R = 26?

I want an answer which will not be related to equilibria and their stability, because I have the same question about the NE6 system in [1]:

x' = y

y’ = z

z’ = -y-xz-yz-a

This system has no equilibrium. What is in there when a = 0.74, which is not in there when a = 0.78?

Reference

[1] Jafari, S., Sprott, J.C., Golpayegani, S.M.R.H. [2013] “Elementary quadratic chaotic flows with no equilibria,” Phys. Lett. A, 377, 699-702.

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