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3.2 Linear Systems
Recall:
We have a system of the form
X MX ,
where Mis a constant 2 2 matrix. The point 0,0 is an
equilibrium point.
Suppose Mhas real eigenvalues λ1, λ2R, with corresponding
eigenvectors V1,V2R2. Then the system has straight-line
trajectories along the lines through 0,0 parallel to V1and V2.
If λ10, the corresponding trajectories move away from 0,0 . If
λ10, the corresponding trajectories move toward 0,0 .
3.2 Linear Systems
Two nonreal complex eigenvalues
If λ1αiβand λ2αiβwith β0, then the
corresponding eigenvectors are also complex, and we cannot plot
them on the xy-plane.
Example. Earlier, we had the system
