System Configuration

Row 1:
Row 2:
Enter matrix coefficients
to see classification
Based on eigenvalues and eigenvectors

Phase Portraits of Linear Systems

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Example Matrices

🎬 Bifurcation (Animated)

A(\mu) = \begin{pmatrix} 0 & 1 \\ -\mu & 4-\mu^2 \end{pmatrix}, \quad \mu \in [-2,2]

Stable Node

\begin{pmatrix} -2 & 0 \\ 0 & -3 \end{pmatrix}

Unstable Node

\begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}

Saddle Point

\begin{pmatrix} 1 & 3 \\ 3 & -1 \end{pmatrix}

Stable Spiral

\begin{pmatrix} -1 & 2 \\ -2 & -1 \end{pmatrix}

Unstable Spiral

\begin{pmatrix} 1 & 2 \\ -2 & 1 \end{pmatrix}

Center

\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}

Star Node

\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}

Defective Node

\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}