CDS - Nullclines

Remember:

Take for example this sytem:$\{\begin{array}{l}{\dot{x}}_1=10x+y-5\\ {\dot{x}}_2=5y\end{array}$To find the nullclines we solve the following eqations:$\dot{x}=0$Since we have only 2 components:$\{\begin{array}{l}{\dot{x}}_1=0\\ {\dot{x}}_2=0\end{array}$Meaning:$\{\begin{array}{l}10x_1+x_2-5=0\\ 5x_2=0\end{array}$From this equation we find the two nullclines:

1. $x_2=-x_1+5$
2. $x_2=0$

Another example:

We have also seen some other examples in 2D, can be useful to understand and visualize the nullclines.

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• IMPORTANT
• In case of linear system we need the nullclines, and eigenvectors, to define the phase space.