proto-guybaa2
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Hi,
i am new here and this is my first problem to post. As you probably know eigenvalues are used to determine the stability of critical points of systems of first-order, autonomous differential equations. I know how the method works for 2x2 systems. For example if the eigenvalues of matrix A are of opposite sign then the critical point is a saddle. And this is asymptotically unstable. My problem is the classification of 3x3 systems. With 3x3 systems you get 3 eigenvalues and three eigenvectors. Finding them is relatively easy. But what is the classification for example if i get 2 positive eigenvalues and one negative? Is this is a node, stable or unstable? So basically i need an overview of the classification of the type and stability for 3x3 systems. Your help is much appreciated!
i am new here and this is my first problem to post. As you probably know eigenvalues are used to determine the stability of critical points of systems of first-order, autonomous differential equations. I know how the method works for 2x2 systems. For example if the eigenvalues of matrix A are of opposite sign then the critical point is a saddle. And this is asymptotically unstable. My problem is the classification of 3x3 systems. With 3x3 systems you get 3 eigenvalues and three eigenvectors. Finding them is relatively easy. But what is the classification for example if i get 2 positive eigenvalues and one negative? Is this is a node, stable or unstable? So basically i need an overview of the classification of the type and stability for 3x3 systems. Your help is much appreciated!