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### Topics - Sabrina (Man) Luo

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##### Ch 9 / Final Review
« on: April 16, 2013, 02:29:29 AM »
As you said that if it is node, then the system is not integrable. However, what will be the way to know more about globally phase portrait?

Another one:We studied energy equation for saddle and centre in non-linear system, when it is integrable, so can we think that if it is integrable, then by looking for energy equation, the centre won't become a spiral?

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##### Quiz 5 / Day Section's Quiz Problem 2
« on: April 03, 2013, 09:12:44 AM »
(2) Find an equation of the form H(x,y)=c satisfied by solutions to
\begin{equation*}
\left\{\begin{aligned}
&dx/dt=2x^2y-3x^2-4y,\\
&dy/dt=-2xy^2+6xy
\end{aligned}
\right.\end{equation*}

3
##### Quiz 5 / Day Section's Quiz - Problem 1
« on: April 03, 2013, 09:11:21 AM »
(1) For the system
\begin{equation*}
\left\{\begin{aligned}
&dx/dt=y+x(1-x^2-y^2),\\
&dy/dt=-x+y(1-x^2-y^2)
\end{aligned}
\right.\end{equation*}
determine all critical points, linearize around each critical point, and determine what conclusion can be made about the nonlinear system at each critical point based on the linearization. Draw a phase portrait for the nonlinear system.

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