Second Order Solution Behavior and Eigenvalues: Three Main Cases For second order systems, the three main cases are: Eigenvalues are real and have opp
{"Image DocumentName": "Second Order Solution Behavior and Eigenvalues: Three Main Cases", "Image ImageDescription": "For second order systems, the three main cases are: Eigenvalues are real and have opposite signs; x = 0 is a saddle point. Eigenvalues are real, distinct and have same sign; x = 0 is a node. Eigenvalues are complex with nonzero real part; x = 0 a spiral point. Other possibilities exist and occur as transitions between two of the cases listed above: A zero eigenvalue occurs during transition between saddle point and node. Real and equal eigenvalues occur during transition between nodes and spiral points. Purely imaginary eigenvalues occur during a transition between asymptotically stable and unstable spiral points.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}