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I have

$f'_1(t)=-af_1(t)f_2(t)+bf_3(t)$

$f'_2(t)=f_1(t)$

$2f'_3(t)=-f_1(t)$

How is it possible to evaluate fixed points of this system of equations and afterwards the stability of these points. I only know how to do it for simple equations like $x_{n+1}=f(x_n)$

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    I get for f_1=f_3=0 and f_2=c. How can i evaluate the stabilit$y$ of the points?2012-11-09

1 Answers 1

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First, calculate fixed points, then analyze the stability of the linearization.

Your fixed point is $f_1 = 0, f_3 = 0, f_2 = p$ if $b \ne 0$ and $p \in \mathbb{R}$.

Next we linearize,

$\begin{pmatrix} -ap & 0 & b\\ 1 & 0 & 0\\ -1/2 & 0 & 0 \end{pmatrix}$

Then calculate the eigenvalues for each $p$ to determine stability near each fixed point.