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.
A question about nonlinear ODE and chaos
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ordinary-differential-equations
chaos-theory
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0There is no accepted definition of chaos, so answers may vary. Also, what do you mean by "after rightful parametrizing"? – 2012-11-06
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0@ChristopherA.Wong multiply or add any term with a number. – 2012-11-06
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0I don't think anybody can prove something on _every 3 dimensional nonlinear ordynary differential equation_. That being said, you can read about the [Lorenz system](http://en.wikipedia.org/wiki/Lorenz_system) – 2012-11-06
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0Surely 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 map – 2012-11-07