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I'm just being curious, but is it true or false, that every 3 dimensional nonlinear ordinary differential equations, after rightful parameterizing, can become chaotic? If not, what kind of 3-D ODE can become chaotic after choosing the right parameter? Please give some reference if possible.

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    Surely the nonlinear ODE with separated variables are not chaotic, I think the Lorenz maps of the phase portrait of the chaotic ODE are concave functions, like a logistic map2012-11-07

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