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BrainHurts
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Homework Statement
[itex]\frac{dU}{dz} = V, \frac{dV}{dz}=k+cU-6U^{2}[/itex] c [itex]\in[/itex] ℝ
Find the fixed points of the system (these are solutions U=U*, V=V* where U*,V* [itex]\in[/itex] ℝ) and determine the value of k so that the origin is a fixed point of the system
Homework Equations
The Attempt at a Solution
I'm not too familiar with dynamical systems but I believe that we want
[itex]\frac{dU}{dz}|_{V=V^{*}} = V^{*} = 0[/itex]
and
[itex]\frac{dV}{dz}| _{U=U^{*}} = k+cU-6U^{2} = k+cU^{*}-6(U^{*})^{2} = 0[/itex]
So we want a value of k so that the origin is a fixed point of the system. I'm not quite sure what this means.