Notes: (please read, press (i) on set to read the entire thing)
This set is revised for clarity and making sure all the terms flow in a straightforward way rather than making them more complex to make it easier to understand.
Note that a value is PURELY ___ means the value must meet the standard requirements of being a ____ type of value (nothing more or less), for example, PURELY imaginary value means it MUST have an imaginary component, no more or no less.
Phase portrait solution classifications for ALWAYS stable and ALWAYS unstable, etc. are just by definition/convention of what they are in math books. Just remember that they are ALWAYS that type of classification.
(handy references: http://www.math.psu.edu/tseng/class/Math251/Phase_portrait_reference_card.pdf, http://wwwf.imperial.ac.uk/metric/metric_public/differential_equations/second_order/qualitative_methods_1.html)
Sources for all images:
My own notes for stable node and unstable node. I am licensing these in the public domain.
http://www.texample.net/media/tikz/examples/PDF/poincare.pdf
(license: no rights reserved)
(source for image: https://commons.wikimedia.org/wiki/File:Phase_Portrait_Stable_Proper_Node.svg, license: public domain)
(source for image: https://commons.wikimedia.org/wiki/File:Phase_Portrait_Unstable_Proper_Node.svg, license: public domain)
_Don't worry about remembering this, just another guide for what you might see online_
A "star" in this set might also be called an improper node in other math classes/online resources/books, etc
A "node" in this set might also be called an improper node in other math classes/online resources/books, etc.