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 Post subject: Rössler systemPosted: Mon, 28 Nov 2011 23:09:39 UTC
 S.O.S. Oldtimer

Joined: Mon, 28 Dec 2009 00:16:28 UTC
Posts: 228
The defining equations are:

dx/dt = -(y + z)
dy/dt = x + ay
dz/dt = b + z(x - c)

where a = b = 0.2 and 2.6 ≤ c ≤ 4.2.

Is there an analytic way of showing that by changing the parameter c, we can get period-1 orbit, period-2 orbit, period-4 oribt, period-8 orbit, etc. and for c > 4.2 we get a chaotic attractor? I know you can construct a bifurcation diagram or use a projection onto the xy-plane and change c, but is there an analytic approach to this problem?

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