I am not sure the name for this is really "degenerate", but consider the following system of non-linear ODEs: \begin{align*} \frac{dx}{dt} & = a(1-x)z-ex, \\ \frac{dy}{dt} & = -axy, \\ \frac{dz}{dt} & = axy - cz. \end{align*} The critical point is $(x,y,z) = (0,y,0)$, for any $y$. But starting from a certain $y$ I end up with another, final one. Is it possible to obtain the final values from the initial values in any way? I would be very thankful if anyone could point me in the right direction.
System of ODEs with a degenerate (?) critical point
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ordinary-differential-equations
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0I have been precisely trying to find some constant of motion by I am not sure how to do this, or of these is some general method for it. Any advice? – 2012-07-09