Khan exercises Maths Tools 1

Fixed Points of a Nonlinear System

New Numbers

The vector field F:R2R2,(y1y2)(10y1+9y25y12+6y1y22)F: \mathbb R^2 \to \mathbb R^2, \begin{pmatrix} y_1 \\ y_2 \end{pmatrix}\mapsto \begin{pmatrix} 10y_1 + 9y_2 \\ 5y_1^2 + 6y_1 y_2^2 \end{pmatrix} defines a system y=F(y)y' = F(y).

Find the fixed point y=(y,1,y,2)(0,0)y_{\infty} = \left({\color{red}y_{\infty,1}},{\color{blue}y_{\infty,2}}\right) \neq (0,0).