3. Consider the system of ODEs given by x' = x2 - y2 and y' = x² + y2 – 1. = (a) Enumerate all equilibria. (b) For each
Posted: Wed May 11, 2022 10:13 pm
3. Consider the system of ODEs given by x' = x2 - y2 and y' = x² + y2 – 1. = (a) Enumerate all equilibria. (b) For each equilibrium, identify the behavior of the dynamics near the equilibrium. In other words, is the equilibrium a source, sink, saddle, center point, spiral source, spiral sink, or something else? Justify your answer (just stating the final result does not earn points).